MEDICAL MEASUREMENTS MATH
WORKBOOK
Community Health Aide/Practitioner Program
Author: Daniel C. Thomas, Curriculum Coordinator, Health Aide Training Center, NSHC
Computer graphics by Michael Faubion and Clifford Hunt, YKHC Media Services.
Formatting assistance from Maureen Murray, Advanced Training Program Coordinator, YKHC CHAP.
Editing suggestions from Jane Allen, Assistant Professor of Mathematics, Kuskokwim Campus, UAF
and Linda Curda, UAF/CHAP Academic Liaison, Kuskokwim Campus, UAF
1/8/01, revised 2/16/01, revised 3/29/02
Copyright 2001 by Daniel C. Thomas
All or parts of this document may be reproduced for educational purposes only.
1
MEDICAL MEASUREMENTS MATH WORKBOOK
Table of Contents
BP CUFF GAUGE .......................................................................................................................................... 3
OXYGEN TANK GAUGES ........................................................................................................................... 7
FRACTIONS ................................................................................................................................................ 10
A 3CC SYRINGE IN TENTHS OF A CC …………………………………………………………………….13
READING A RULER IN FRACTIONS OF AN INCH .......................................................................................... 16
CUTTING UP A PIE ………………………………………………………………………………………..19
A CLOCK’S FACE ...................................................................................................................................... 21
A BABY SCALE ......................................................................................................................................... 22
AN ADULT SCALE ..................................................................................................................................... 23
PENICILLIN SYRINGES ............................................................................................................................... 25
Bicillin ……………………………………………………………………………………………………………25
Wycillin ................................................................................................................................................ 29
THE EIGHTH OF AN INCH ........................................................................................................................... 32
SIXTEENTHS AND THIRTY-SECONDS OF AN INCH ………………………………………………………..36
SUMMARY OF READING A RULER IN INCHES ……………………………………………………………..37
THE METRIC SYSTEM : CENTIMETERS AND MILLIMETERS ……………………………………………. 41
DECIMALS ………………………………………………………………………………………………...43
ADDING DECIMALS AND TYLENOL DROPS DOSAGES …………………………………………………….47
DOLLARS AND CENTS ……………………………………………………………………………………51
THOUSANDTHS …………………………………………………………………………………………...52
DIGOXIN DOSES …………………………………………………………………………………………..53
THERMOMETERS …………………………………………………………………………………………57
FIFTHS …………………………………………………………………………………………………….57
BACK TO THERMOMETERS ………………………………………………………………………………...61
READING A HYPOTHERMIA THERMOMETER ………………………………………………………………63
ANOTHER HYPOTHERMIA THERMOMETER ………………………………………………………………..64
SYRINGE MATH …………………………………………………………………………………………...67
VOLUME: CC AND ML ……………………………………………………………………………………...67
CONCENTRATIONS …………………………………………………………………………………………69
3 CC SYRINGE ……………………………………………………………………………………………...73
5 CC SYRINGE ……………………………………………………………………………………………...77
1 CC TB SYRINGE ………………………………………………………………………………………….82
1 CC EPINEPHRINE TUBEX SYRINGE ……………………………………………………………………….92
50 UNIT INSULIN SYRINGE ………………………………………………………………………………...97
100 UNIT INSULIN SYRINGE ……………………………………………………………………………...101
SUMMARY OF READING A SYRINGE ……………………………………………………………………...107
2
Medical Measurements
We are always measuring things as we take care of patients. To do this correctly, we must look at how
measuring devices use marks to show different amounts. We will look at whole numbers first (numbers
that haven’t been divided into parts smaller than 1, such as decimals or fractions). Examples of whole
numbers are 1, 2, 3, 4, 5, and so on, all the numbers that we learned to count as small children.
BP Cuff Gauge
The gauge on a BP cuff has little marks to show the different blood pressure values. Only some of the
marks are numbered. We have to figure out what the numbers are for the other marks. The marks that
are numbered are 20, 40, 60, 80, 100, 120, and so on.
140
160
180
200
120
100 SPHYGMOMANOMETER 220
80
240
260
60
280
40
20
300
fig001
First we must note that there are two sizes of marks, big ones and little ones. There is a big mark at each
of the numbers as well as halfway between each of the numbers. For instance, there is a big mark
halfway between the big mark at 80 and the big mark at 100.
140
160
180
200
120
100 SPHYGMOMANOMETER 220
80
240
260
60
280
40
20
300
fig002
3
We need to figure out what the number is for that big mark. It would make sense that it should be the
number that comes halfway between 80 and 100. To figure out what number that would be, it helps to
draw a diagram called a number line, which shows the numbers as we would count them from left to
right.
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
fig003
Looking at this diagram, we can see that the number 90 comes halfway between 80 and 100.
halfway
1/
2
1/
2
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
fig004
Therefore, 90 must be the number for the big mark that is halfway between 80 and 100 on the BP gauge.
140
160
180
200
120
90
100 SPHYGMOMANOMETER 220
80
240
260
60
280
40
20
300
fig005
4
In the same way, we can figure out each of the big marks between the numbers on the BP gauge. It turns
out that each is a multiple of ten (the numbers that you get when you count by tens: 10, 20, 30, 40, 50,
60, 70, 80, 90, 100, 110, 120, and so on).
150
130
110
140
160
180
200
120
100 SPHYGMOMANOMETER 220
90
80
70
240
260
60
280
40
20
50
300
30
fig006
The next step is to figure out what the small marks are in between the big marks that we numbered above.
There are 4 small marks in between each pair of big marks. The rule to follow to figure this out is that
marks like this are usually ones or twos. So we count the marks by ones and count them by twos and see
which comes out right.
If we try counting by ones first, between 80 and the big mark that we know is 90, this is what we find:
100
(90)
80
80
fig007
We can see that this doesn’t come out right because we are counting “85” when we reach the 90 mark.
5
If we try counting by twos, we get this:
100
(90)
80
80
fig008
This comes out right, so each of the small marks is worth 2, not 1.
This is a simple way to figure out the little marks on any measuring device: count the marks by ones or
twos and see which comes out right. This is true for whole numbers and decimals. Fractions are
different, as we will see later.
Another way to figure out the small marks is to note that they divide the space between 80 and 90 into 5
equal parts. The space between 80 and 90 on the BP gauge is equal to 10 (BP is measured in millimeters
of mercury, so this 10 actually represents 10 millimeters of mercury). The little marks divide the 10 into
5 equal parts.
100
(90)
1
80
fig009
If we divide 10 into 5 equal parts (10  5), we find that each of the 5 equal parts is 2 (10  5 = 2). So
each little mark on the BP gauge indicates 2 millimeters of mercury.
6
Oxygen Tank Gauges
There are usually two gauges on an oxygen tank regulator: one shows LPM (liters per minute), the other
shows psi (pounds per square inch). Liters per minute (LPM) measures how fast the oxygen is coming
out of the tank (how many liters of oxygen come out in one minute). This is called the flow rate. One
common type of flow gauge looks like this:
8
6
10
OXYGEN
12
4
2
CALIBRATED
FOR NO. 27 DRILLED
ORIFICE
14
15
LITERS PER MINUTE
fig010
If the needle points to the 2, oxygen is leaving the tank at the rate of 2 liters per minute.
The big marks indicate the number of liters per minute. Only half of the big marks have
a number (2, 4, 6, 8, 10, 12, 14, 15). We have to figure out the numbers for the big
marks that don’t have a number.
For instance, there is a big mark halfway between 2 and 4. We know that the number 3 comes halfway
between the numbers 2 and 4, so that is the correct number for the big mark between 2 and 4.
8
6
10
OXYGEN
12
4
CALIBRATED
FOR NO. 27 DRILLED
ORIFICE
2
3
14
15
LITERS PER MINUTE
fig011
Since the rest of the gauge is arranged the same way, we can number the dial all the way around by
inserting the numbers that come between the numbers listed on the gauge.
7
8
5
6
10
OXYGEN
12
4
3
2
CALIBRATED
FOR NO. 27 DRILLED
ORIFICE
14
15
LITERS PER MINUTE
fig012
7
The psi (pounds per square inch) gauge measures the pressure of the oxygen in the tank. The more
oxygen that is put in the tank, the more pressure it puts on the inside of the tank, measured in pounds of
pressure per square inch of tank surface. A full tank has a pressure of 2,000 pounds per square inch
(2,000 psi).
The psi gauge has big marks numbered 500, 1000, 1500, 2000, 2500, and so on.
FULL
UL
OPEN
CYLINDER
VALVE SLOWLY
OXYGEN
fig013
We need to figure out what the little marks are between the big marks. As with the BP gauge and other
measuring devices, the marks probably are worth one or two, or in this case it will be 100 or 200.
First we will try counting out the marks by 100s, starting at the 500 mark.
1000
900
800
700
600
500
Oxygen tank
pressure guage
psi
fig014
8
This comes out right, so each little mark is indeed 100 psi. If it hadn’t come out right, we would have
tried counting by 200s next, like so:
1500
1300
1100
900
700
500
Oxygen tank
pressure guage
psi
fig015
This doesn’t come out right, since we are counting “1500” when we reach the number 1000 on the gauge.
Therefore, each little mark cannot be 200.
9
Fractions
A fraction is a number that represents an amount less than 1. If you take something such as a pie or
candy bar and divide it into pieces, each piece is a fraction of the whole. Fractions used frequently in
everyday language include the half, third, and quarter.
1
2
is a fraction (“one half”) that means that something has been divided into 2
equal parts, and we have 1 of those parts.
The bottom number of a fraction states how many equal parts the whole was divided into:
1
2
the whole number was divided into 2 equal parts
The top number of a fraction states how many of the equal parts we have:
1
2
we have 1 of the 2 equal parts.
Pretend that this is a candy bar that has been cut in half.
Now pretend that we have one of those pieces (half of the candy bar)
1
2
we have 1 of the 2 equal parts.
the candy bar is divided into 2 equal parts.
10
For another example, pretend this is a candy bar that has been cut into 10 equal pieces.
1
2
3
4
5
6
7
8
9
10
Now pretend that we have 5 of those equal pieces.
1
2
3
4
5
This is
5
10
5
(five tenths) of the candy bar.
10
we have 5 of the 10 equal parts.
the candy bar is divided into 10 equal parts.
5
1
(five tenths) and
(one half) actually are the same amount, for 5 is half of 10.
10
2
To show this, we take the candy bar and divide it in half.
1–
2
1–
2
fig020
Then we divide the candy bar into 10 equal pieces.
1
2
3
4
5
6
7
8
9
10
fig021
11
Each half has 5 of the 10 equal pieces.
1
2
3
4
5
1
–
2
fig022
So,
1
5
(one half) =
(five tenths).
2
10
1
–
2
1
–
2
1
2
3
4
5
6
7
8
9
10
5
—
10
5
—
10
fig023
12
A 3 cc Syringe in Tenths of a cc
For a good example of halves and tenths, look at your 3 cc syringe. The 3 cc syringe has 2 sets of
markings; make sure you are looking at the “cc” markings (the marks on the right side).
1/
2
1
11/2
2
21/2
3 cc
fig024
We see that each cc is labeled with a whole number (1, 2, and 3).
Each half of a cc is labeled also (½, 1½, 2½).
Each cc is also divided into 10 equal parts by the smallest marks. If we start at the “zero” (empty) line
and count the marks up to 1, we will be counting “10” when we reach 1 cc.
zero
1
2
3
4
5
6
7
8
9
10
1/
2
1
fig025
13
If we divide a cc into 10 equal parts, each part is one tenth of a cc. Therefore, each little
mark is one tenth (
1
) of a cc.
10
zero
1/
10
2/
10
3/
10
4/
10
5/
10
6/
10
7/
10
8/
10
9/
10
10/
10
We know this is correct because we are counting
1/
2
1
fig026
10
(ten tenths) when we reach 1 cc on the syringe.
10
10
(ten tenths) means that we have all 10 of the 10 equal parts of the whole,
10
which is one whole cc (1 cc).
10
=1
10
1/
2
10/
10
1
fig027
14
The other clue that we have counted the marks correctly is that we are counting
we reach the
5
(five tenths) when
10
1
mark on the syringe. 5 is indeed half of 10, so we know we are counting correctly.
2
5
1
=
10
2
5/10
1/
2
1
fig028
15
Reading a Ruler in Fractions of an Inch
Another example of fractions that we find in our work is reading inches on a ruler, such as the paper
measuring tape:
1
2
3
4
5
6
fig029
The biggest lines are numbered, representing inches.
1 inch
1
2 inches
3 inches
2
3
4
5
6
fig030
On the ruler below, the next biggest line (halfway between the two numbers) divides 1 inch into two equal
parts. Therefore, it marks
1
an inch.
2
1
–
2
0
1
2
1
fig031
we have 1 of the 2 equal parts.
the inch is divided into 2 equal parts.
The 2 equal parts are both
1
an inch long (see below).
2
1
–
2
0
1
–
2
1
fig032
16
Each of the half inch segments is divided in half by another shorter line (see below).
0
1
fig033
If we study these 3 lines between 0 and 1, we see that they divide the inch into 4 equal parts (see below).
1 2 3 4
0
Each of the 4 equal parts is one fourth (
1
4
1
fig034
1
fig035
1
) of an inch.
4
we have 1 of the 4 equal parts.
the inch is divided into 4 equal parts.
1
–
4
0
1
–
4
1
–
4
1
–
4
– (one fourth) of an inch.
The first line marks 1
4
2
The second line marks –
4 (two fourths) of an inch.
– (three fourths) of an inch.
The third line marks 3
4
– (four fourths) of an inch
The fourth line marks 4
4
which is all 4 of 4 equal parts (one whole inch).
1
– 2
–
4 4
0
3
–
4
4
–
4
1
fig036
17
Another name for a fourth is a quarter, so we say “one quarter of an inch”. When describing money,
there are 4 quarters in a dollar: a quarter is one fourth (
1
) of a dollar.
4
18
Notice that the middle line marks
1
2
of an inch as well as
of an inch.
4
2
1
2
=
4
2
2
–
4
1
–
2
0
1
0
1
fig037
fig038
If you divide the whole inch into 4 equal parts and take 2 of those parts, you have
1
–
4
0
1
of the whole.
2
1
–
4
1
–
2
2
–=1
–
4 2
1
fig039
Cutting Up a Pie
Another popular way to look at fractions is by cutting up a pie.
The first cut of a knife across a pie divides it in half, into 2 equal parts. Each part is one half (
1
) of the
2
pie.
1
–
2
1
–
2
fig040
The second cut of a knife across a pie divides each of the halves in half, giving 4 equal parts of the pie.
1 2
3 4
fig041
19
If a whole is divided into 4 equal parts, each of the 4 parts is one fourth of the whole.
1
–
4
1
–
4
1
–
4
1
–
4
fig042
Each half of the pie has 2 of the 4 equal parts of the pie. Each half of the pie has 2 fourths of the pie.
1
–
4
1
–
4
1
–
4
1
–
4
fig043
2 of the 4 equal parts is
1
of the pie.
2

2
1
of a pie =
of the pie.
4
2
2
1
=
4
2
1
2
) and two fourths ( ) are the same amount.
2
4
1
2
5
and
and
are all the same amount.
2
4
10
One half (
1
– of
2
=
1
–
2
1
– of
2
=
2
–
4
10 1
9
1
– of
2
1
2
8
2
3
7
6 5
4
=
3
5
5
–
10
4
fig044
20
A Clock’s Face
Another use of fourths and halves that we use in everyday life is in describing parts of an hour when
telling time. Remember that there are 60 minutes in one hour. If we look at the minutes of a clock’s
face, it can be divided up just like a pie.
30 minutes is half an hour (30 is half of 60).
11 12 1
10
2
3
9
8
4
7 6 5
fig045
1
30 minutes = half an hour ( )
2
15 minutes is a quarter of an hour (15 is one quarter of 60).
11 12 1
10
2
3
9
8
4
7 6 5
fig046
1
15 minutes = a quarter of an hour ( )
4
45 minutes is three quarters (
3
) of an hour (45 is three quarters of 60).
4
11 12 1
10
2
9
3
8
4
7 6 5
fig047
3
45 minutes = three quarters of an hour ( )
4
21
A Baby Scale
Halves and quarters are the fractions that are encountered when reading a scale.
0
2
4
0
1
2
3
fig048
fig049
pounds on an adult scale
ounces on an infant scale
If we look at the ounces on a baby scale, we see that each ounce is divided in half by a long mark halfway
between the whole numbers.
1/
2
0
11/2
1
21/2
2
3
fig050
In addition, each half of an ounce is divided in half by a shorter mark. As we know from cutting up a pie,
half of a half is a fourth.
1
– of
4
1
– of
2
1
– of
a pie
2
=
a pie
fig051
Half of a half ounce is one fourth of an ounce (½ of ½ oz = ¼ oz).
1
– 1
–
4 2
0
1
2
3
fig052
22
We also know that if we divide a whole into 4 equal parts, each part is one fourth (
1
4
1
) of the whole.
4
we have 1 of the 4 equal parts.
the ounce is divided into 4 equal parts.
So, the shortest marks are fourths or quarters of an ounce.
1
– 2
– 3
– 4
–
4 4 4 4
0
1
2
3
Baby Scale (in ounces)
fig053
1
2
2
1
mark can also be counted as the
mark, for we know that
=
.
2
4
4
2
4
Also note that
is the same as 1 (all 4 of the 4 equal parts equal the whole ounce)
4
1
Remember, if something is divided into 2 equal parts, each part is a half ( ).
2
1
If something is divided into 4 equal parts, each part is a fourth ( ) (one quarter).
4
Note that the
An Adult Scale
On the adult scale, the markings are almost the same. The differences are that we are talking pounds
instead of ounces, and the scale is numbered every 2 pounds.
0
2
4
Adult Scale (in pounds)
fig054
There is a long mark halfway between each of the numbered marks. For instance, there is a long mark
halfway between 2 and 4. Since the number 3 is halfway between the numbers 2 and 4, that is the
number for the long mark halfway between 2 and 4.
3
0
2
4
fig055
23
The number for each long mark between the numbers on the scale can be figured out the same way.
3
1
0
2
5
4
fig056
Once we know that, the other markings are the same as on the baby scale, except in fractions of a pound
1
instead of fractions of an ounce. The longer mark halfway between the whole numbers is one half ( ) of
2
a pound.
1/
2
11/2 21/2 31/2
0
2
4
3
1
fig057
The shortest marks divide each pound into 4 equal parts and therefore are fourths of a pound.
1
– 2
– 3
– 4
–
4 4 4 4
0
2
1
Note again that
4
fig058
2
1
4
is also and that is also 1.
4
2
4
24
Penicillin Syringes
Injectable penicillins (Bicillin and Wycillin) come in prefilled syringes. We will look at Tubex syringes
below. These types of penicillin are measured in units rather than milligrams. Reading these syringes is
made easier by the fact that the CHAM dose will be either a whole syringe, three fourths of a syringe, half
a syringe, or a fourth of a syringe. These are the only measurements that we need to learn on these
syringes.
Bicillin
The Bicillin syringe below has 1,200,000 units of Bicillin (one million two hundred thousand units, which
can also be called 1.2 million units). As with any measuring device, the first step to reading it is to figure
out what the little marks mean. On these syringes there is only one mark, which is a black line across the
middle of the syringe. This line across the middle of the syringe divides it in half.
BICILLIN L-A 1,200,000 units
1
–
2
1
–
2
Half of 1,200,000 units is 600,000 units.
fig059
1,200,000  2 = 600,000
1,200,000 units
600,000 units
600,000 units
fig060
To check our math, we can add 600,000 to 600,000 and see if it equals 1,200,000.
600,000
+ 600,000
1,200,000
25
So we now know how much Bicillin is in half a syringe, as indicated by the line across the middle of the
syringe. Since doses on this syringe can be in fourths also, we need to figure out where fourths are on
this syringe.
We learned earlier that a fourth of a pie is a half of a half.
1
– of
2
1
– of
a pie
2
1
– of
4
a pie
=
fig061
In the same way, on this syringe, a fourth will be half of a half. We need to imagine a line dividing each
half of the syringe in half.
1
–
4
1
–
2
3
–
4
fig062
The next step is to figure out how many units are in a fourth of the syringe and three fourths of the
syringe.
If we divide each half (600,000 units) into two equal parts, each part will be a fourth of the syringe and
will be 300,000 units. 600,000  2 = 300,000
600,000 units
300,000 300,000
fig063
26
To check our math, we can add 300,000 to 300,000 to see if it equals 600,000.
300,000
+ 300,000
600,000
Therefore, one fourth of 1,200,000 units is 300,000 units. If we divide 1,200,000 units into 4 equal parts,
each will be 300,000 units. 1,200,000  4 = 300,000.
1
–
4
1
–
4
1
–
4
1
–
4
300,000 300,000 300,000 300,000
fig064
300,000
+ 300,000
+ 300,000
+ 300,000
1,200,000
1
3
of the 1,200,000 unit syringe. If the order is for 900,000 units, this should be
4
4
of the syringe (300,000 + 300,000 + 300,000 = 900,000).
So, 300,000 units is
300,000 300,000 300,000
900,000
3
–
4
fig065
27
Or we can think of it as adding 300,000 units (
1
1
of a syringe) to 600,000 units ( of a syringe)
4
2
(300,000 + 600,000 = 900,000).
600,000
300,000
900,000
fig066
These are the only doses of Bicillin given in the CHAM:
1
300,000 units ( syringe)
4
1
600,000 units ( syringe)
2
3
900,000 units ( syringe)
4
1,200,000 units (1 whole syringe)
1
–
4
1
–
2
3
–
4
1
300,000 600,000 900,000 1,200,000
fig067
28
Wycillin
The 600,000 unit Wycillin Tubex syringe is similar to the Bicillin Tubex. There is a black line that
divides the syringe in half:
WYCILLIN
600,000 units
1
–
2
Half of 600,000 units is 300,000 units.
1
–
2
fig068
600,000  2 = 300,000.
600,000 units
300,000 units
300,000 units
fig069
To check our math, we can add 300,000 to 300,000 and see if it equals 600,000.
300,000
+ 300,000
600,000
If we divide each half (300,000 units) into 2 equal parts, each will be 150,000 units.
300,000 units
150,000 150,000
fig070
29
To check our math, we can add 150,000 to 150,000 to see if it equals 300,000.
150,000
+ 150,000
300,000
Therefore, one fourth of 600,000 units is 150,000 units. If we divide 600,000 units into 4 equal parts,
each will be 150,000 units. 600,000  4 = 150,000.
1
–
4
1
–
4
1
–
4
1
–
4
150,000 150,000 150,000 150,000
fig080
150,000
+ 150,000
+ 150,000
+ 150,000
600,000
1
3
of the 600,000 unit syringe. If the order is for 450,000 units, this should be
4
4
of the syringe (150,000 + 150,000 + 150,000 = 450,000).
So, 150,000 units is
150,000 150,000 150,000
450,000
Or we can think of it as adding 150,000 units (
3
–
4
fig081
1
1
of a syringe) to 300,000 units ( of a syringe)
4
2
(150,000 + 300,000 = 450,000).
300,000
450,000
150,000
fig082
30
These are the only doses you are likely to give with the 600,000 unit Wycillin syringe:
1
150,000 units (
syringe)
4
1
300,000 units (
syringe)
2
3
450,000 units (
syringe)
4
600,000 units (1 whole syringe)
1
–
4
1
–
2
3
–
4
1
150,000 300,000 450,000 600,000
fig083
31
The Eighth of an Inch
Usually halves, fourths, and tenths are the only fractions we have to deal with in measurements. There is
one more fraction that we sometimes encounter, usually when measuring in inches.
1
That is the eighth ( ).
8
If we look at a pie again, recall that it is cut first in half,
1
–
2
1
–
2
fig084
then in fourths.
1
–
4
1
–
4
1
–
4
1
–
4
fig085
But usually a fourth of a pie is too big, so we cut each fourth in half to make a total of eight equal parts.
8 1
7
6
2
3
5 4
fig086
The whole pie is now cut into eight equal parts, so each part is one eighth (
1
8
1
of a pie).
8
we have 1 of the 8 equal parts.
the pie is divided into 8 equal parts.
32
1
–
8
1
–
8
Notice that two eighths of a pie (
1
–
8
1
– 1
–
8 8
1
–
8
1
–
1
– 8
8
1
–
8
fig087
2
) (2 of the 8 parts) is the same as one fourth of a pie:
8
1
–
8
=
1
–
4
fig088
2
1
=
8
4
1 of the 4 equal parts is the same as 2 of the 8 equal parts.
Half of a fourth is an eighth.
1
– of
2
Also notice that four eighths of a pie (
1
–
8
1
–
8
1
–
8
1
–
8
1
–
4
is
1
–
8
fig089
4
) (4 of the 8 parts) is the same as one half of the pie.
8
=
1
–
2
fig090
4
1
=
8
2
1 of 2 equal parts is the same as 4 of 8 equal parts.
33
Back to the inch ruler, recall that the line halfway between zero and 1 marks
1
of an inch.
2
1
–
2
0
1
If we look at the line halfway between zero and the
fig091
1
1
inch line, we recall that this is
of an inch.
2
4
Half of a half is a fourth.
1
–
4
1
–
2
0
1
fig092
The inch system of measurement is organized in fractions that keep dividing the length in half. So, an
inch is first divided in half. Then the half inch is divided in half to make fourths. Then the fourth is
divided in half to make eighths. Half of a fourth of an inch is one eighth of an inch.
1
–1
–
84
1
–
2
0
1
fig093
Another approach is to look at the 7 longer lines between 0 and 1. Ignore the shorter lines for now.
1234567
0
1
fig094
34
We see that the 7 lines divide the inch into 8 equal parts (eighths of an inch).
12345678
0
1
fig095
The first line marks 1–8 (one eighth) of an inch.
The second line marks 2–8 (two eighths) of an inch.
The third line marks 3–8 (three eighths) of an inch.
And so on, up to 1 inch
8
The eighth line marks –8 (eight eighths) of an inch
which is all 8 of 8 equal parts (one whole inch).
1
–2
–3
–4
–5
–6
–7
–8
–
88888888
0
Note again that
1
fig096
2
1
4
1
is the same as
, and
is the same as
.
8
4
8
2
0
2
–
8
4
–
8
1
–
4
1
–
2
1
fig097
Two examples of measurements in eighths of an inch:
1
- For suturing, we are taught to place the stitch
of an inch from the edge of a
8
wound.
5
- For a subcutaneous injection, we use a 25 gauge
inch needle.
8
35
Sixteenths and Thirty-Seconds of an Inch
Many rulers will go even smaller and divide an inch into 16 equal parts (sixteenths of an inch) (
1
).
16
Half of an eighth is a sixteenth. If an inch is divided into 8 equal parts and we divide each of the parts in
half, there will be 16 equal parts.
1—
2—
3—
4
—
1616
1616
0 1– 2–
1
88
fig098
Some rulers divide the sixteenth of an inch in half to make thirty-seconds of an inch. See the metal desk
ruler below.
1 —
2 —
3
—
32 32 32
0
1
fig099
Note on the metal desk ruler that each line marks half the length of the next longer line.
1
1
—
—
32 = half as long as 16
1
1
—
–
16 = half as long as 8
1
– = half as long as 1
–
8
4
1
– = half as long as 1
–
4
2
1
– = half as long as 1 inch
2
0
1
fig100
36
Summary of Reading a Ruler in Inches
The key to reading a ruler (and any other measuring device) is to figure out what the little marks are
before trying to measure anything. With inches, the two ways to do this have been demonstrated above:
1. Count how many equal parts the inch is divided up into by the marks. For example, if the
1
marks divide the inch into 8 equal parts, each mark is
of an inch.
8
2. Or, keep dividing the lengths in half to see which length equals which mark. As shown
1
1
1
1
1
1
above, half of
is
, half of
is
, half of
is
, and so on. The marks on a
2
4
4
8
8
16
ruler are given different lengths to help us see this. The longest line between zero and 1 is in
1
the middle and equals
.
2
1
–
2
0
1
fig101
If we look for the next longest line, we find that there are two the same length. One is halfway between
1
1
1
3
zero and
, and the other is halfway between
and 1. They mark
and
.
2
2
4
4
4
2
1
Recall that
=
and = 1.
4
2
4
1
–
4
0
3
–
4
1
–=2
–
2 4
1
fig102
37
There are four of the next longest line, in the middle of each of the fourths of an inch.
1
3
5
7
They mark
,
,
, and
.
8
8
8
8
1
–
8
0
Note that
2
1
= ,
4
8
4
1
= ,
8
2
3
–
8
2
–
8
5
– 7
–
8 8
4
–
8
6
–
8
1
fig103
8
6
3
= , and
=1.
8
4
8
38
The next longest lines are sixteenths of an inch, dividing the eighths in half.
1
3
5
7
They mark
,
,
,
, and so on.
16 16 16 16
1 —
3 —
7
—
16 16 16
2
–
016
Note that
2
1
= ,
16 8
4
2
1
= = ,
16
8
4
15
—
16
8
–
16
6
3
= ,
16 8
1
fig104
8
4
2
1
16
=
= = , and so on, up to
= 1.
16
8
4
2
16
All of these lines can be seen on the plastic head circumference tape below.
1
–
2
1
–
4
1
1
2
1
–
8
2
3
4
5
1
—
16
3
6
7
4
8
9
10
5
11
12
6
13
14
15
fig105
If a ruler has even shorter lines, those will be thirty-seconds of an inch, dividing the sixteenths in half.
See the drawing of a metal desk ruler below.
Note that
1
2
=
,
32 16
1 —
2 —
3
—
32 32 32
31
—
32
0
1
2
1
4
=
= ,
32 16 8
3
6
=
,
32 16
fig106
4
2
1
8
32
=
= = , and so on, up to
= 1.
8
4
32 16
32
39
So, to read a ruler in inches, figure out what fraction each line represents, starting with the longest and
working down to the shortest.
In the medical professions, most people use millimeters for tiny measurements rather than sixteenths or
thirty-seconds of an inch. Many rulers or measuring tapes have both systems of measurement, such as
the plastic head circumference tape below.
1
—
16 of an inch
1
1
2
2
3
4
5
3
6
7
4
8
9
10
5
11
12
6
13
14
15
1 millimeter
fig107
A common problem with using any ruler or measuring tape is not knowing if the marks are for inches or
centimeters (often they are not labeled; it is assumed that we can tell which is which). On the paper
measuring tape below, note that an inch is more than twice as big as a centimeter. Inches are on one side
of the tape, and centimeters are on the other side.
1 inch
1
2
3
4
fig108
1 centimeter
10
20
30
40
50
60
70
80
90
fig109
We will look at centimeters and millimeters next.
40
The Metric System: Centimeters and Millimeters
In the medical fields it is very common to use the metric system for measuring length (how long things
are) rather than inches.
The word “metric” comes from the word “meter”, which is a measurement of length about 39 inches
long, a little longer than a yard. In the USA we are used to the “English” system of measuring length
(inches, feet, yards). But in medicine, the metric system is used frequently for measuring length in terms
of centimeters (abbreviated "cm") and millimeters (abbreviated "mm").
The metric system is used by most of the rest of the world because it is easier to work with. Everything
is in multiples of ten (ones, tens, hundreds, thousands, tenths, hundredths), whereas the English system
has strange combinations of numbers, such as eighths of an inch, 12 inches in 1 foot, 3 feet in 1 yard, and
so on. Most rulers have both inches and centimeters on them since we use both systems of measuring
length. Our growth charts have both also.
With the metric system, we have to know a few special terms.
1
“Centi” means one hundredth (
).
100
Century means 100 years.
1
A cent is
of a dollar.
100
A centimeter (cm) is one hundredth of a meter. If we divide a meter (about 39 inches) into 100 equal
parts, each one is a centimeter, a hundredth of a meter. It is about this long: ------- and is found on most
rulers and measuring tapes along with inches, on the opposite edge or the backside. Usually the
centimeters and inches are not labeled; we are expected to know which is which by their different size
and markings.
Usually a baby’s head circumference is measured in cm, although it can be measured in inches also. The
measuring tape has both.
1
).
1000
Millenium means 1000 years.
“Milli” means one thousandth (
A milliliter (ml) is one thousandth (
1
) of a liter.
1000
A millimeter (mm) is one thousandth of a meter. If we divide a meter (about 39 inches) into 1000 equal
parts, each one is a millimeter, a thousandth of a meter.
There are 10 millimeters (mm) in each centimeter (cm). If we divide a centimeter (cm) into 10 equal
parts, each one is a millimeter (mm), for a millimeter (mm) is one tenth of a centimeter (cm). A
millimeter (mm) is about this long: - .
41
Here is the length 10 mm:
. We can see this on any ruler or measuring tape that shows 10 little
marks for each centimeter. The little marks divide a centimeter into 10 equal parts, each of which is 1
1
mm. A mm is one tenth ( ) of a cm.
10
10 mm
1 cm
fig110
Because a mm is so small, it is useful for measuring small things, such as:
- PPD skin tests.
- the size of pupils.
- skin growths or lesions.
- small wounds.
Rulers or measuring tapes that show millimeters will usually have a longer mark halfway between the
centimeter numbers. This mark is for half of one centimeter (½ cm).
11/2
1
/2
0
1
2
fig111
As we have seen before, if a whole is divided into 10 equal parts (in this case it is a cm divided into 10
mm), half of those 10 parts is 5.
½ of a centimeter is 5 millimeters.
5mm
1
/2 cm
1
2
fig112
42
Decimals
Decimals are just another way of writing fractions. They both measure parts that are smaller than the
whole.
A decimal is a special type of fraction where the whole has been divided into tenths, hundredths,
thousandths, and so on. See the number 1,532.467 below:
1,532.467
whole
decimals
numbers
fig113
The number above shows that a decimal is written as a decimal point (which looks like a period), with
the whole numbers to the left of the decimal point and the decimal numbers to the right of the decimal
point. When read out loud, the decimal point is read as “point”. The number above should be read as
“one thousand five hundred thirty-two point four six seven”.
4
6
7
With this number, we have 4 tenths ( ), 6 hundredths (
), and 7 thousandths (
).
10
100
1000
6
7
—
—
4 100
1000
—
10
1,532.467
fig114
As we see from the number above, each space to the right of the decimal has the value of a particular
fraction, and the bottom number of these fractions is the number 10 with more zeros added to it as we go
to the right:
6
7
—
—
4 100
—
1000
10
.467
fig115
43
Each of the spaces to the right of the decimal point is called a decimal place and is named for the fraction
that it represents:
.__
the tenth decimal place. Any number here is equal to a fraction with 10
on the bottom (tenths), such as:
3
.3 =
(3 tenths)
10
5
.5 =
(5 tenths)
10
.__ __
the hundredth decimal place. Any number here is equal to a fraction
with 100 on the bottom (hundredths), such as:
4
.04 =
(4 hundredths)
100
9
.09 =
(9 hundredths)
100
.__ __ __
the thousandth decimal place. Any number here is equal to a
fraction with 1000 on the bottom (thousandths), such as:
5
.005 =
(5 thousandths)
1000
1
.001 =
(1 thousandth)
1000
If there is just a decimal and no whole number, a lone zero is placed to the left of the decimal point to
emphasize where the decimal is located:
.1 should be written as 0.1 (read as "zero point one").
This lone zero to the left of the decimal point does not change the value of the number.
44
Serious medication errors are made if we mix up where the decimal point goes, for this will increase or
decrease the amount of drug given by ten times or a hundred times.
For instance, we have to be careful not to confuse 1.0 with 0.1 or with 0.01:
1.0 = one whole
0.1 = one tenth
0.01 = one hundredth
If the correct dose of epinephrine is 0.1 cc and we give 1.0 cc instead, we have given 10 times the
correct dose. We gave 1 cc instead of one tenth of a cc.
Examples of decimals:
0.1
= one tenth (something is divided into 10 equal parts. We have 1 of the 10
equal parts).
0.05 = five hundredths (something is divided into 100 equal parts. We have 5 of
the 100 equal parts).
$0.03 = three hundredths of a dollar (a dollar is divided into one hundred equal parts
[cents]. We have three of the hundred parts.) Dollars and cents are
written in decimals, so everyone is at least a little familiar with the decimal
system.
0.007 = seven thousandths (something is divided into 1000 equal parts. We have 7
of the 1000 parts).
Some examples of decimals combined with whole numbers:
1.2
= one and 2 tenths ("one point two")
$1.20
= one dollar and 20 cents (20 cents = 20 hundredths of a dollar)
3.5
= three and 5 tenths ("three point five")
3.05
= three and 5 hundredths ("three point zero five")
3.005 = three and 5 thousandths ("three point zero zero five")
Adding a zero on the right hand side of a decimal does not change its value: 1.2 = 1.20
Also, a zero on the right end of a decimal can be removed without changing its value: 2.50 = 2.5
This brings us to the important point that 0.1 (
1
10
) and 0.10 (
) are the same amount.
10
100
100
) is also the same amount as 0.1 and 0.10. Adding zeros to the right end of a decimal
1000
1
10
100
does not change its value. Why the fractions
,
, and
are equal will be explained in more
10 100
1000
detail later.
In fact, 0.100 (
45
Here are some common fraction/decimal equivalents:
(an equivalent is something equal to something else)
1
2
4
5
50
=
=
=
= 0.5 = 0.50 =
2
4
8
10
100
1
2
25
=
= 0.25 =
4
8
100
1
2
20
=
= 0.2 = 0.20 =
5
10
100
46
Adding Decimals and Tylenol Drops Dosages
Sometimes we may need to add decimal numbers to figure out medication dosages. One example is with
Infant Tylenol Drops.
Infant Tylenol Drops are measured in a dropper that is marked at 0.4 ml and 0.8 ml.
0.8
ml
0.4
ml
fig116
If the patient’s dose is 0.4 ml or 0.8 ml, there is no problem finding the dose on the dropper. However,
for bigger kids, the CHAM dose may be 1.2 ml or 1.6 ml or 2.0 ml. We will need to do some adding to
figure out how much to give with the dropper.
The key to adding decimals is to line up the decimal points so that the different decimal places are also
lined up. For example, to add up 1.2, 15.07, 0.05, and 0.1, we would need to line up the numbers like
this:
Tens
Ones
Decimal Point
Tenths
Hundredths
+
1.2
1 5.0 7
0 .0 5
0.1
fig117
The decimal point in your answer will lined up directly below the other decimal points.
47
When we have the decimal places lined up, then we add up each column, starting on the right and
working our way to the left, much the same as we do for whole numbers. When necessary, we carry over
numbers from one column to the next column on the left, just like with whole numbers. With the
numbers above, first we add up the hundredths column:
Tens
Ones
Decimal Point
Tenths
Hundredths
+
1.2
1 5.0 7
0 .0 5
0.1
12
fig118
We need to carry the 1 over to the tenths column.
Tenths
Hundredths
+
1
1.2
1 5.0 7
0 .0 5
0.1
2
carry
the 1
fig119
Now we add up the tenths column:
Tenths
Hundredths
+
1
1.2
1 5.0 7
0 .0 5
0.1
4 2
fig120
48
There is nothing to carry over to the ones column. Now we add the ones column and the tens column just
like we usually add whole numbers.
Tens
Ones
Decimal Point
Tenths
Hundredths
+
1.2
1 5.0 7
0 .0 5
0.1
1 6 .4 2
fig121
If we add a zero to the right end of 1.2 and 0.1, this is exactly the same as adding dollars and cents.
Tens
Ones
Decimal Point
Tenths
Hundredths
$1 .2
$1 5 .0
$0.0
+ $0.1
$1 6 . 4
0
7
5
0
2
fig122
49
The Tylenol dropper is easier because there is only the tenths decimal place to deal with.
tenths
tenths


0.4 ml
0.8 ml
If the child is 25 pounds, the CHAM dose for Tylenol Drops is 1.2 ml. The CHAM makes it easier by
making all its doses combinations of 0.4 ml and 0.8 ml . So, what combination of 0.4 ml and 0.8 ml adds
up to 1.2 ml?
We can try some combinations and see what we get:
0.4 + 0.4 = ?
If we line up the decimal points, this adds up easily:
0.4
+0.4
0.8 (we add the numbers in the tenths column)
This doesn’t equal 1.2, so we need to try another combination.
0.8 is less than 1.2, so let’s try adding another 0.4 to 0.8:
0.8 + 0.4 = ?
If we line up the decimal points, it adds up like this:
0.8
+0.4
1.2 (we add the numbers in the tenths column and carry the 1
over to the ones column)
Therefore, to get 1.2 ml we start with 0.8 ml and add 0.4 ml.
1.2 ml
=
0.8
ml
0.4
ml
+
0.8
ml
0.4
ml
fig123
50
Dollars and Cents
Our familiarity with dollars and cents can help us to understand decimals better.
$0.50 = half a dollar (50 is half of 100 cents)
0.50 = 0.5 (50 hundredths = 5 tenths)
5
1
Therefore, 0.5 =
=
.
10
2
(This all makes sense if we note that 50 is half of 100, 5 is half of 10, and 1 is half of 2.)
50
5
1
=
=
100
10
2
$0.10 =
10
(10 cents out of 100 cents in a dollar)
100
10 cents is a dime.
There are 10 dimes in a dollar, so a dime is
$0.01 =
1 cent
1
(one tenth) of a dollar.
10
1
(1 cent out of 100 cents in a dollar)
100
= $0.01 =
1
1
of a dollar = one hundredth of a dollar (0.01 =
)
100
100
1 dime = $0.10 =
10
of a dollar = ten hundredths of a dollar = 10 cents
100
1 dollar = $1.00 =
100
of a dollar = 100 cents
100
0.10 is the same as 0.1 because we can drop any zeros on the right end of a decimal.
Therefore, a dime (10 cents) can be regarded in two ways:
10
1. It is 0.10 or
(ten hundredths) of a dollar.
100
(10 out of the 100 cents that make up a dollar)
1
2. It is also 0.1 or
(one tenth) of a dollar.
10
(1 of the 10 dimes that make up a dollar)
51
So,
0.10 = 0.1 (1 dime is
1
of a dollar)
10
2
of a dollar)
10
3
0.30 = 0.3 (3 dimes are
of a dollar)
10
4
0.40 = 0.4 (4 dimes are
of a dollar)
10
Likewise, 0.20 = 0.2 (2 dimes are
0.50 = 0.5 (5 dimes or a 50 cent piece are
5
1
of a dollar, which is
of a
10
2
dollar)
0.25 = a quarter of a dollar (25 cents is
1
25
of a dollar, which is
of a dollar)
4
100
Thousandths
We can take our study of decimals even further by adding one more zero to the right end of the decimal
0.20, making it 0.200 (200 thousandths). Remember the value of each decimal place, shown below:
0.200
fig124
Adding the extra zeros to the right end of the decimal does not change its value.
Therefore, 0.2 = 0.20 = 0.200
2
20
200
=
=
10
100
1000
It is a common mistake to think that the extra zeros on the right end of a decimal make it bigger.
However, as we have discussed above, this is not true.
For instance, 0.100 is smaller than 0.2 .
0.20 (
20
200
) = 0.200 (
)
100
1000
0.200 (
200
100
) is twice as much as 0.100 (
).
1000
1000
Therefore, 0.20 is twice as much as 0.100
52
Digoxin Doses
This brings us to an important medication, digoxin. Digoxin is a medicine that is taken to slow and
strengthen the heart beat. It is probably taken by at least one patient in your village. If the patient takes
too much, serious problems can develop with the heart, even death. So, giving the correct dose is very
important.
Digoxin tablets come in 3 sizes:
5
mg)
10
25
0.25 mg (
mg)
100
125
0.125 mg (
mg)
1000
0.5 mg (
If one isn’t familiar with decimals, 0.125 might look bigger than 0.25 or 0.5, but actually it is the
smallest. This is easier to recognize if we remember the value of each decimal place (see below):
0.000
fig125
The key here is to remember that the value of the decimal place gets smaller as we move to the right from
the decimal point. Hundredths are much smaller than tenths. Thousandths are much smaller than
hundredths.
53
To understand the different sizes of the digoxin doses, we must look at each decimal place of the different
numbers.
0.5 mg = 5 tenths
0.25 mg = 2 tenths and 5 hundredths
0.125 mg = 1 tenth, 2 hundredths, and 5 thousandths
First let’s look at the tenth decimal place for each number:
tenths
0.5 mg
0.25 mg
0.125 mg
5
)
10
2
0.2 ( )
10
1
0.1 ( )
10
0.5 (
Since tenths are much bigger than hundredths or thousandths, looking at what is in the tenth decimal place
is a big clue as to which decimal number is bigger or smaller.
Now let’s look at the hundredth decimal place for each of the 3 numbers:
hundredths
We can add a zero to the right end of 0.5
50
) without changing its value.
100
25
0.25 (
)
100
12
0.12 (
)
100
0.5 mg
0.50 (
0.25 mg
0.125 mg
It makes sense that 0.5 = 0.50 because 0.5 =
5
50
1
and 0.50 =
, and both are the same as
10
100
2
(5 is half of 10; 50 is half of 100).
Looking at the tenth and hundredth decimal places of these numbers, we can easily see that 0.50 is the
biggest and 0.12 is the smallest.
0.5 mg
0.25 mg
0.125 mg
50
)
100
25
0.25 (
)
100
12
0.12 (
)
100
0.50 (
54
Now let’s look at the thousandth decimal place for each of the 3 numbers:
thousandths
0.5 mg
0.25 mg
0.125 mg
500
)
1000
250
0.250 (
)
1000
125
0.125 (
)
1000
0.500 (
We can add another zero to the right end of this
decimal without changing its value.
For 0.5, we can put zeros in the hundredth decimal place and the thousandth decimal place (making it
0.500) without changing its value. It makes sense that 0.5 = 0.500 because:
5
,
10
500
0.500 =
,
1000
0.5 =
and both are the same as
1
(5 is half of 10; 500 is half of 1000).
2
For 0.25, we can put a zero in the thousandth decimal place (making it 0.250) without changing its value.
It makes sense that 0.25 = 0.250 because:
25
,
100
250
0.250 =
,
1000
0.25 =
and both are the same as
1
1
1
(25 is
of 100; 250 is
of 1000).
4
4
4
By expressing all the digoxin dose numbers in thousandths, it is clear which number is bigger or smaller.
0.5 mg
0.25 mg
0.125 mg
500
)
1000
250
0.250 (
)
1000
125
0.125 (
)
1000
0.500 (
1
of the whole) (500 + 500 = 1000)
2
1
0.250 = 250 thousandths ( of the whole) (250 + 250 + 250 + 250 = 1000)
4
1
0.125 = 125 thousandths ( of the whole) (125+125+125+125+125+125+125+125 = 1000)
8
0.500 = 500 thousandths (
55
When the digoxin doses are all written in thousandths of a mg, it is obvious that 0.500 mg is the biggest
number, then 0.250 mg, then 0.125 mg. When comparing decimals, always look at the tenths place of all
the numbers, or the tenths and hundredths together, or the tenths, hundredths, and thousandths together.
When dealing with digoxin doses, we need to recognize that 0.25 mg is half of 0.5 mg.
Two 0.25 mg tablets are the same amount of digoxin as one 0.5 mg tablet.
0.25 mg (
1
1
1
mg) + 0.25 mg ( mg) = 0.5 mg ( mg)
4
4
2
0.25 mg
+ 0.25 mg
0.50 mg (same as 0.5 mg)
To add decimal numbers (see above), we line up the decimal points and add each column, starting on the
right, similar to how we add whole numbers.
Also with digoxin, we must recognize that 0.125 mg is half of 0.25 mg.
Two 0.125 mg tablets are the same amount of digoxin as one 0.25 mg tablet.
0.125 mg + 0.125 mg = 0.25 mg
0.125 mg
+ 0.125 mg
0.250 mg (same as 0.25 mg)
56
Thermometers
We use decimals all the time when we measure temperature.
98.6 is read as “ninety eight point six” degrees.
This means that the temperature is 98 degrees plus another six tenths of a degree (98
6
).
10
The placement of the decimal point is crucial, since we don’t want to confuse 102 (one hundred and two
degrees) with 100.2 (one hundred point two degrees).
To understand the marks on a glass thermometer (and a 5 cc syringe), we need to understand fifths in
fractions and decimals.
Fifths
1
is a fraction (one fifth) that means that something has been divided into 5 equal parts and we have 1 of
5
those parts.
1
2
3
4
5
Pretend that this is a candy bar that has been cut into 5 equal pieces.
fig126
Now pretend that we have one of those pieces (one fifth of the candy bar).
1
5
fig127
we have 1 of the 5 equal pieces.
the candy bar is divided into 5 equal pieces.
If we had 2 of the pieces, it would be written
2
(two fifths).
5
If we had 3 of the pieces, it would be written
fig128
3
(three fifths).
5
fig129
And so on.
5
5
= five fifths (the whole candy bar), so
= 1.
5
5
57
Here is how this can be changed to decimals:
1
5
1 of the 5 equal parts ( ) is the same as 2 of 10 equal parts (
2
). See the cut up
10
candy bars below:
a candy bar cut into
10 equal parts
a candy bar cut into 5
equal parts
1
–
5
1
–
5
1
–
5
1
–
5
1
–
5
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
1
/10
/10
1
/10
1
/10
1
/10
1
/10
1
/10
1
/10
1
/10
1
/10
1
f fig130
fig131
The candy bars have been cut to show that
1/
5
1
2
of the candy bar is the same as
.
5
10
1
/10
/10
1
fig132
58
We can see here that 2 of the 10 equal parts of a whole (
2
1
) is the same as
.
10
5
In a candy bar that is cut into 10 equal pieces, there are 5 equal sets of 2 pieces each.
5 equal sets of 2 parts each
1
2
3
4
5
fig133
2
1
) is the same as
.
10
5
1
2
1
2
So,
=
; and
= 0.2 (the decimal way to write
).
5
10
5
10
2 of the 10 equal parts of a whole (
Another way to look at it is in terms of dollars and dimes. 10 dimes equal 1 dollar.
If we divide the 10 dimes into 5 equal groups, each group will be one fifth of a dollar, and each of the five
groups will have 2 dimes.
10 dimes divided into 5 equal groups of 2 each:
fig134
2
of a dollar (2 of the 10 dimes that make up a dollar)
10
1
and 2 dimes also equal
(one fifth) of a dollar (1 of 5 equal groups of 2 dimes each).
5
So, 2 dimes equal
2
1
=
10
5
59
To put it in dollars and cents,
2 dimes = $0.20 (20 cents),
so $0.20 =
1
(of a dollar)
5
0.20 is the same as 0.2 because we can drop the zero on the right.
Therefore, 0.2 =
1
5
2
1
(2 of 10 parts) =
(1 of 5 parts)
10
5
Using the same example of dimes and dollars,
2
5
3
6 dimes = $0.60 = 0.6 =
5
4
8 dimes = $0.80 = 0.8 =
5
5
10 dimes = $1.00 = 1.0 =
or 1 whole dollar
5
4 dimes = $0.40 = 0.4 =
To relate this to reading a 5cc syringe or glass thermometer, if we have a whole unit of measurement
(such as 1 cc on a syringe or 1 degree on a thermometer) and it is divided into five equal parts, each part
will be one fifth of the whole and will be read as follows:
0
0.2
0.4
0.6
0.8
1.0
fig135
These markings are what we see on a 5 cc syringe.
0
0.2
0.4
0.6
0.8
1.0
1
2
fig136
60
Back to thermometers
A regular glass thermometer looks something like this:
96
98
100
2
4
106
fig137
The arrow points to an extra mark which is 98.6, the average normal oral temperature.
We can see that the numbers “2” and “4” must stand for 102 and 104, since they come between numbers
100 and 106 on the thermometer.
If we ignore the mark with the arrow for a moment, we see that there is a long mark halfway between
each of the numbers. For example, there is a long mark halfway between 96 and 98.
96
98
100
2
4
106
fig138
Since the number 97 comes halfway between the numbers 96 and 98 when we count, it must be the
number for the long mark that is halfway between 96 and 98.
97
96
98
100
2
4
106
fig139
Since the rest of the thermometer is arranged the same way, we can number all the long lines by inserting
the numbers that come between the numbers already printed on the thermometer.
97
96
99
98
101
100
103
2
105
4
106
fig140
61
Now we have to figure out what the littlest marks are. If we count the marks between 96 and 97, we find
that there are 4, and they divide the 1 degree between 96 and 97 into 5 equal parts.
1 2 3 4 5
96
97
98
fig141
1
5
Therefore, each of those 5 equal parts is one fifth ( ) of a degree. We know that the fraction
1
can be
5
written in decimals as 0.2 .
1
= 0.2
5
Remember that this is because
the decimal 0.2
1
2
2
is the same amount as
, and
can be written as
5
10
10
.
Therefore, if a degree of temperature is divided up into 5 equal parts, each part is 0.2 degrees.
0.2 0.2 0.2 0.2 0.2
96
97
98
fig142
When something like a thermometer is marked off in fifths, we count off the marks by twos.
.2 .4 .6 .8
96
97
98
fig143
Now we can see that the extra long mark is indeed 98.6
because it is the average normal oral temperature.
. This temperature gets its own special mark
.2 .4 .6 .8
96
97
98
99
98.6
100
fig144
62
Reading a Hypothermia Thermometer
A glass hypothermia thermometer is divided up differently than a regular thermometer. This is because it
covers a much wider range of temperature than a regular thermometer. It is marked from 75 to 105 (or
70 to 100), and there isn’t enough room to mark every two tenths of a degree.
There are several different hypothermia thermometers made; we will look at just two.
On the thermometer below, we see that it is numbered every 5 degrees, at the longest marks.
75
80
85
90
95
100
105
fig145
As we saw when reading a ruler, when we have several different sized marks, we need to figure out what
the biggest marks stand for, then the next biggest, then the next biggest, working our way down to the
smallest marks.
If we look at the next biggest marks on the thermometer, we see that there are 4 between each number,
dividing the space in between the numbers into 5 equal amounts:
1
2
3
4
5
75
80
fig146
Since there are 5 whole numbers from 75 to 80 when we count, we can guess that each of those medium
sized marks is 1 whole degree. To check this, we need to count it out:
76
77
78
79
75
80
fig147
It comes out right, so each medium sized mark is indeed 1 degree.
Next, we need to figure out what the smallest marks are for. Since each degree is divided in half by the
smallest marks, each small mark must be worth
751/2
75
76
1
a degree.
2
761/2 771/2 781/2 791/2
77
78
79
80
fig175
63
Another Hypothermia Thermometer
The other hypothermia thermometer we will look at is more difficult. If your thermometer doesn’t look
like this, you can skip this section (turn to the next section on Syringe Math).
Here is how the other thermometer is marked:
70
5
80
5
90
5
100
fig176
The long mark halfway between 70 and 80 is labeled “5”. When we count, the number halfway between
70 and 80 is 75, so we know that the 5 between 70 and 80 on the thermometer means 75. Likewise, the 5
halfway between 80 and 90 is 85, and the 5 halfway between 90 and 100 is 95.
75
70
5
85
80
5
95
90
5
100
fig177
Now we need to figure out the numbers for the other long marks that don’t have a number.
70
5
80
5
90
5
100
fig178
64
These unnumbered long marks are halfway between the 10’s (70, 80, 90, 100) and the 5’s. There are 5
degrees between 70 and 75, and the long mark halfway between 70 and 75 divides those 5 degrees in half.
half
of 5
70
half
of 5
5
80
5
5
degrees
degrees
5
90
5
100
fig179
Therefore, the space between each of the unnumbered long marks must equal half of 5 degrees.
half
of 5
70
half
of 5
5
80
5
5
degrees
degrees
5
90
5
100
fig180
If we divide 5 in half (5  2), we get 2 ½ . Therefore, each unnumbered long mark is 2 ½ degrees. Add
the 2 ½ to the number on the thermometer to find the value of the unnumbered long marks.
721/2
70
771/2
5
821/2
80
871/2
5
921/2
90
971/2
5
100
fig181
Now comes the question of what the little marks are worth. Perhaps the easiest way to figure that out is
to note that the little marks between 70 and 75 divide those 5 degrees into 10 equal parts:
1 2 3 4 5 6 7 8 9 10
70
75
5 degrees
fig182
65
Imagine that the 5 degrees were marked like this:
1 degree
70
71
72
73
74
75
fig183
To make this into 10 equal parts, we have to divide each of the 5 degrees in half. That gives us 10 parts
of ½ degrees each.
1
/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2
70
71
72
73
74
75
fig184
Now look at the hypothermia thermometer again. It is divided the same way, with each ½ degree
marked with a little mark.
71
1
/2
70
72
1
/2
73
1
/2
721¦2
74
1
/2
1
/2
75
fig185
This thermometer is unusually difficult, but you will need to be able to read it if this is the thermometer
you have to work with and you have a cold patient.
66
Syringe Math
Syringes use a combination of fractions and decimals, so an understanding of these is necessary to use
syringes safely. To help you understand the explanation of each syringe, get one of each syringe from
your clinic supply to look at while going through this workbook.
Volume: cc and ml
Syringes measure volume (amount of liquid). The unit of measurement with syringes is usually the cc or
ml.
A cc is the same as an ml (milliliter) and is the amount of liquid that would fill a little box (cube) with
sides 1 cm (centimeter) long.
This box is 1 centimeter on all sides.
This makes it 1 cubic centimeter (a cube with sides 1 cm long).
“cc” is the abbreviation for “cubic centimeter”.
1 cm
1 cm
fig186
Since an ml (milliliter) is the same volume as a cc, that little box will hold 1 ml of liquid. An ml is also
one thousandth (
1
) of a liter (the big IV bags hold 1 liter of liquid).
1000
The “milli” in millimeter means one thousandth. There are 1000 milliliters (ml) in a 1 liter IV bag. If
we divided the fluid in a 1 liter IV bag into 1000 equal parts, each part would be 1 milliliter or ml.
1 milliliter =
1
of a liter
1000
1 milliliter of liquid = 1 cubic centimeter of liquid
1 ml = 1 cc
Some syringes are labeled in cc; others are labeled in ml. Since cc and ml are the same, it doesn’t matter
which term we use, and we often use them both.
1/2
1
1
/2 ml
1ml
PHENOBARBITAL
11/2
2
21/2
3cc
1/
2 ml
1ml
Epinephrine
fig188
fig189
67
An important point on syringes: note that the 3 cc and the 1 cc TB syringe have another set of markings
besides cc. These other marks are labeled “M” for minims, another unit of volume measurement that we
never use. Don’t confuse minims with cc for they are completely different amounts.
minims cc
minims cc
M
2
M
10
.2
4
1/2
.3
6
1
20
30
.5
10
.6
2
.7
.8
21/2
14
3 cc
3 cc Syringe
.4
8
11/2
12
40
.1
16
fig190
.9
1.0cc
TB syringe
fig191
68
Concentrations
Drugs that come in liquid form are measured in volume of liquid (ml or cc) and in mg (the dry weight of
the drug that is mixed into the liquid). Think of this like Tang powder mixed with water.
Mg stands for milligram. The gram is the metric system unit of measurement of weight (in medicine we
use both the English weight measurements of pounds/ounces and the metric weight measurements of
1
) of a gram (remember that “milli”
1000
1
1
means “one thousandth”), just like a millimeter is
of a meter, and a milliliter is
of a liter.
1000
1000
grams/kilograms/milligrams). A milligram is one thousandth (
The amount of dry drug mixed into the liquid is written as a concentration, expressed as mg per ml.
Mg per ml tells us how many milligrams of dry drug powder are mixed in each ml of liquid.
Think again of dry Tang powder mixed in water. We have to mix a certain amount of powder with a
certain amount of water to get the correct concentration that tastes good. If we put in too much powder
(or not enough water), the Tang liquid is too concentrated and tastes too strong. If we put in not enough
powder (or too much water), the liquid is too weak.
For example, amoxicillin suspension when mixed with the correct amount of water is in a concentration
of 250 mg per 5 ml. This means that in each 5 ml of liquid, there is 250 mg of dry amoxicillin powder.
Another way to write it is 250 mg/5 ml.
250 mg of dry
amoxicillin powder
5 ml of liquid amoxicillin suspension
fig192
Children’s Motrin comes in a concentration of 100 mg per 5 ml (100 mg of dry Motrin powder in each 5
ml of suspension). Most liquid drugs, oral and injectable, are labeled this way. One exception is
medicines measured in units, such as Bicillin, Wycillin, insulin, and oxytocin.
69
Injectable drugs are usually labeled with the number of mg in 1 ml (mg per ml). For example, your
injectable phenobarbital comes in a concentration of 130 mg per ml. This means there is 130 mg of dry
phenobarbital powder in 1 ml of the injectable medicine. Injectable diphenhydramine (Benadryl)
comes in a concentration of 50 mg per ml.
1/ ml
2
1ml
PHENOBARBITAL
130 mg per ml
1/ ml
2
fig193
1ml
dyphenhydramine
50 mg per ml
fig194
It is important to be aware that drugs come in all sorts of different concentrations. In fact, a single drug
may come in more than one concentration. For example, Augmentin suspension comes as 250 mg per 5
ml and as 125 mg per 5 ml. Infant Tylenol Drops are 100 mg per ml, but Children’s Tylenol
Suspension is 160 mg per 5 ml. So when we give liquid medicines, we have to be sure to have the right
drug and the right concentration of that drug. Fortunately, most village clinics stock only one
concentration of each drug to avoid confusion. The concentration is always written on the container.
fig195
70
Sometimes when giving injectable drugs we have a dose in mg and have to figure out how much that
would be in ml. For instance the doctor’s order might be for 40 mg furosemide. Furosemide comes in
a 2 ml ampule with a concentration of 10 mg per ml. We would need to figure out how much to give in
ml. It helps to draw a picture of the ampule showing how many ml are in the ampule and how many mg
are in each ml.
1 ml
10 mg
1 ml
10 mg
fig196
______________
a 2 ml ampule
with 10 mg
in each ml
Drawing a picture like this helps prevent getting mixed up with all the numbers of ml, mg, and mg per ml.
As we can see by adding up the amounts in the drawing above, the 2 ml ampule has 20 mg total of
furosemide. The doctor has ordered 40 mg, so we will draw more pictures until we have a total of 40 mg of
furosemide.
1 ml
10 mg
1 ml
10 mg
a 2 ml ampule
1 ml
10 mg
1 ml
10 mg
a 2 ml ampule
_____________
2 ampules
= 4 ml total
and 40 mg total
fig196
fig196
71
Another example would be an order for 5 mg of morphine. Morphine comes in a Tubex syringe with
1 ml of liquid and a concentration of 10 mg per ml. First we draw a picture showing this.
1 ml
10 mg
fig199
_____________
1 ml with
10 mg in each ml
The drawing helps us to see that we have got 10 mg morphine total. Now we need to figure out how to
get 5 mg. We know that 5 is half of 10, so we can start by drawing a picture of the 10 mg of dissolved
morphine divided in half.
5 mg
1 ml
10 mg
5 mg
fig200
By dividing the 10 mg in half, we have also divided the 1 ml of liquid in half. Half of an ml is ½ ml.
1 ml
1/ ml
2
5 mg
1/ ml
2
5 mg
10 mg
fig201
_____________
two ½ ml amounts,
each with 5 mg
of morphine
The drawing helps to visualize the amounts and figure out the answer: 5mg of morphine is ½ ml.
1/ ml
2
5 mg
fig202
72
3 cc Syringe
A 3 cc syringe is marked ½ cc, 1 cc, 1 ½ cc, 2 cc, 2 ½ cc, and 3 cc.
1/
2
1
1 1 /2
2
2 1 /2
3cc.
fig203
½ is a fraction that means 1 cc is divided into 2 equal parts, and we are looking at 1 of those parts:
1
2
we have 1 of the 2 equal parts.
the cc is divided into 2 equal parts.
All the whole cc and half cc volumes are numbered on the 3 cc syringe. Now we need to figure out how
much volume each of the small marks is. First we count them.
zero
1
2
3
4
5
6
7
8
9
10
1/
2
1
fig204
73
There are 10 marks from zero to 1 cc. The marks divide each cc into 10 equal parts.
1
2
3
4
5
6
7
8
9
10
1/
1
When 1 cc is divided into 10 equal parts, each part is
1
10
2
fig205
1
(one tenth) of a cc:
10
we have 1 of the 10 equal parts.
the cc is divided into 10 equal parts.
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
2
1
fig206
74
Syringe markings are usually read in decimals, so we need to review what decimals are equal to tenths.
Recall that the decimal place for tenths is just to the right of the decimal point as shown below:
tenths
0.0
Therefore, the fraction
1
is the same as the decimal 0.1 .
10
1
cc = 0.1 cc.
10
Therefore, each of the 10 equal parts (tenths of a cc) = 0.1 cc.
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
1/
2
1
fig207
75
This should be double-checked by counting the marks from zero to 1 cc to make sure they add up to 1.
Start at zero and give each mark a number, using the decimal numbers that equal tenths (0.1, 0.2, 0.3, 0.4,
and so on).
zero
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1/
2
1
fig208
As can be seen above, the marks do add up to 1 when given the value of 0.1 or
1
(one tenth) of a cc
10
each.
We know we are on the right track if we are at 0.5 when we reach the ½ cc mark.
0.5
1/
2
1
fig209
5
Remember that 0.5 =
(five tenths).
10
5
means we have 5 of the 10 equal parts of a cc. 5 is half of 10.
10
5
1
1
Therefore,
=
and 0.5 =
.
10
2
2
So, by counting the little marks from zero to 1 on the 3 cc syringe, we have shown that they add up to 1 cc
if given the value of 0.1 cc each. Therefore, the volume of liquid between each little mark on the 3 cc
syringe is 0.1 cc (one tenth of a cc).
76
5 cc Syringe
Looking at the 5 cc syringe, we see that each cc is numbered.
1
2
3
4
5cc
fig210
Now we need to figure out how much volume each of the small marks is.
First we count the marks from zero to 1 cc.
1
zero
1
2
3
4
5
fig211
77
There are 5 marks from zero to 1 cc.
These marks divide each cc into 5 equal parts.
1
2
3
4
5
1
fig212
When 1 cc is divided into 5 equal parts, each is
1
5
1
(one fifth) of a cc.
5
we have 1 of the 5 equal parts.
the cc is divided into 5 equal parts.
1
1/
5
1/
5
1/
5
1/
5
1/
5
fig213
Syringe markings are usually read as decimals, so we need to review what decimals are equal to fifths.
Recall the decimal places as shown below:
0.000
78
To change the fifths on the syringe into decimals, we must first change the fifths into tenths (which can
1
1
then be written in decimal form). The dotted lines below divide each cc in half. By dividing each
5
5
cc in half, we now have 1 cc divided into 10 equal parts (tenths of a cc).
1/
5
1/
5
1/
5
1/
5
1
1/
5
fig213
From this we see that
1/
1
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1/
10
1
2
=
:
5 10
5
2/
10
1/
5
2/
10
1/
5
2/
10
1/
5
2/
10
1/
5
2/
10
fig215
2
is the same as the decimal 0.2 . Recall that the first space to the right of the decimal
10
2
point is the tenths decimal place, so a 2 in the tenths decimal place (0.2) is the same as 2 tenths ( ).
10
The fraction
tenths
0.2
So, a fifth on the 5 cc syringe is the same as 2 tenths, which written in decimals as 0.2 .
1
2
=
= 0.2
5
10
79
We, then, have figured out that each little mark on the 5 cc syringe is 0.2 cc.
1
1/
5
0.2cc
1/
5
0.2cc
1/
5
0.2cc
1/
5
0.2cc
1/
5
0.2cc
fig216
This should be double-checked by counting the marks from zero to 1 cc to make sure they add up to 1 cc.
Start at zero. The volume of between zero and the first little mark is 0.2 cc, so the first little mark is
counted as 0.2 .
0.2
1
fig217
The volume between each of the little marks is 0.2 cc, so when counting a mark, add 0.2 to the number of
the mark before it.
1
0.2
0.4
0.6
0.8
1.0
fig218
Note that this is like counting by twos (2, 4, 6, 8, 10). The marks do add up to 1 when given the value of
0.2 cc each.
80
Recall that this is the same way we count the marks on a regular glass thermometer.
.2 .4 .6 .8
96
97
98
99
100
fig219
So, by counting the little marks from zero to 1 on the 5 cc syringe, we have shown that they add up to 1 cc
if given the value of 0.2 cc each. Therefore, the volume of liquid between each little mark of the 5 cc
syringe is 0.2 cc (one fifth of a cc).
81
1 cc TB Syringe
This syringe is labeled in decimal numbers, showing tenths of a cc, adding up to 1 cc total.
1
10
2
.2 =
10
3
.3 =
10
4
.4 =
10
.1 =
.1
.2
.3
.4
.5
.6
.7
.8
(one tenth) of a cc
(two tenths) of a cc
(three tenths) of a cc
(four tenths) of a cc, and so on.
(Note that the zero to the left of the decimal points has been left out. Recall that
0.1 = .1).
Doses on this syringe will usually be in tenths of a cc (0.1 cc, 0.2 cc, 0.3 cc, and
so on), easy to find since the tenths are all numbered. Example doses are 0.1 cc
for a PPD, 0.5 cc for a DPT shot, and 0.3 cc for epinephrine. The most common
problem encountered with this syringe is getting confused about where the
decimal point is. For instance, a person could confuse 1.0 cc with 0.1 cc and 0.01
cc.
.9
1.0 cc
fig220
It is important to know what the tiny marks are so that we don’t get them confused with the tenth marks.
To figure out how much volume each of the tiny marks is, first we have to count the marks from zero to
.1 cc.
.1
zero
1
2
3
4
5
6
7
8
9
10
fig221
82
We find that there are 10 tiny marks from zero to .1 cc.
These marks divide each tenth (0.1) into 10 equal parts.
1
2
3
4
5
6
7
8
9
10
.1
fig222
If there are 10 tenths of a cc in 1 cc and each tenth has 10 tiny equal parts, there are 100 of the tiny equal
parts in 1 cc (10 x 10 = 100).
fig223a
fig223b
1
.1
.1
.2
.2
.3
.3
.4
.4
.5
.5
.6
.6
.7
.7
.8
.8
.9
.9
1.0 cc
1.0 cc
2
3
4
5
6
7
8
9
10
10 Tenths of a cc
x
10 tiny equal parts in each tenth
= 100 equal parts of 1 cc.
83
If 1 cc is divided into 100 equal parts, each of the 100 parts is
1
100
1
of a cc.
100
we have 1 of the 100 equal parts.
1 cc is divided into 100 equal parts.
.1
1/
100 cc
1/
100 cc
1/
100 cc
1/
100 cc
1/
100 cc
1/
100 cc
1/
100 cc
1/
100 cc
1/
100 cc
1/
100 cc
fig224
The fraction
1
can be written as the decimal 0.01.
100
tenths
hundredths
0.01
Note the similarity to dollars and cents:
1
$0.01 = one cent =
of a dollar. There are 100 cents in one dollar ($1.00).
100
So, the volume between each of the tiny marks is 0.01 cc (one hundredth of a cc).
.1
.01 cc
.01 cc
.01 cc
.01 cc
.01 cc
.01 cc
.01 cc
.01 cc
.01 cc
.01 cc
fig225
84
This should be double checked by counting the marks from zero to 0.1 to make sure they add up correctly.
Start at zero. The volume between zero and the first tiny mark is 0.01 cc, so the first tiny mark is counted
as 0.01 (“point zero one”).
.01
.1
fig226
Since the volume between each of the tiny marks is 0.01 cc, count each mark by adding 0.01 to the
number of the mark before it.
.1
.01
.02
.03
.04
.05
.06
.07
.08
.09
.10
fig227
Remember that hundredths are like pennies. 10 pennies added together equal $0.10 (ten cents) which is
the same as $0.1, one tenth of a dollar.
In the same way, 10 hundredths added together equal 0.10 , which is the same as 0.1.
85
Although doses on this syringe are usually 1 cc or tenths of a cc, rarely a Health Aide might be given an
order to give an unusual dose such as 0.05 cc epinephrine to an infant.
5
0.05 cc =
(five hundredths) of a cc
100
tenths
hundredths
0.05
Since this is a very small amount, you would definitely use the 1 cc TB syringe in order to be accurate.
0.05 cc is 5 hundredths of a cc, which should be 5 of the tiny marks on the syringe.
.05
.1
.2
.3
fig228
Note that the .05 mark is longer than the other marks between zero and .1 cc. There is a longer mark
halfway between each of the numbers on the syringe. Each is 0.05 (5 hundredths) more than the number
before it.
.05
.1
.15
.2
.25
.3
.35
.4
fig229
86
For instance, the long line halfway between 0.2 and 0.3 is 0.25. This makes sense if we remember that
0.2 (2 tenths) is the same as 0.20 (20 hundredths). If we add 0.05 to 0.20, that makes 0.25 .
0.20
+0.05
0.25
0.25
.1
.2
0.20
.05
.3
fig230
It is important to understand clearly that .05 is a smaller amount than .1 .
If both numbers are expressed as hundredths, it is more obvious which is bigger.
To change .1 to hundredths, we just add another zero on the right: .1 = .10
.10
.1
.2
5
)
100
10
.1 = .10 = (
)
100
fig231
.05 = (
Now it is clear that .05 is smaller than .1 .
.05
.10
.1
.2
fig232
87
This is another example of how the position of the decimal point greatly changes the size of the number.
If a person confused .05 cc with .5 cc, the infant would get .5 cc of epinephrine, 10 times the proper dose
of .05 cc. This might cause serious problems for the baby.
.05
.1
.2
.3
.4
.5
.5
.6
.7
.8
.9
1.0 cc
fig233
If you have time, the doctor may prefer you to give epinephrine in a 1 cc TB syringe rather than the 1 cc
Tubex syringe, because the TB syringe is more accurate.
88
Another drug that should be given with a 1 cc TB syringe is terbutaline. Terbutaline is given to stop
premature labor with a dose of 0.25 cc SQ.
25
0.25 cc =
(25 hundredths) of a cc
100
tenths
hundredths
0.25
Since each tiny mark is one hundredth of a cc, 0.25 should be 25 of those tiny marks.
25 marks
.1
.2
.3
fig234
Another way to find 0.25 on the syringe is to remember that 0.25 is the same as
0.20 + 0.05 : 0.20
+0.05
0.25
Knowing this, we can find 0.20 on the syringe (which would be the 0.2 mark, because 0.2 is the same as
0.20) and count 5 marks past it.
.1
.20
.25
.2
.3
.4
.5
fig235
89
One way to make sure we are not making a big mistake is to remember that 0.25 cc is
1
of 1 cc. So, we
4
can eyeball the syringe and see if the plunger is at about one fourth.
0.25 =
1
of 1 cc
4
1/
4
.1
.1
.2
.2
.25
1/
4
.3
.3
.4
.4
.5
1/
4
= 1/4
2/
4
.6
.5
.6
.7
.7
3/
4
1/
4
.8
.8
.9
.9
1.0 cc
4/
4
1.0 cc
fig236
90
A common error with this syringe is to put the plunger at the decimal point of the number rather than at
the proper line on the syringe.
Example: the amount ordered is 0.1 cc.
fig237
As we can see with the pictures above, with the plunger at the decimal point of 0.1 we have a slightly
bigger volume than 0.1 cc, which is marked with the long line.
91
1 cc Epinephrine Tubex Syringe
Looking at this prefilled Tubex syringe, we see that it is divided into several equal parts, marked with
lines. The two thick lines are labeled ½ ml and 1 ml.
fig238
Now we need to figure out how much volume each of the other marks is.
First we count the marks from zero to 1 ml.
1
2
3
4
5
6
7
8
9
10
fig239
92
There are 10 marks from zero to 1 ml. These marks divide the 1 ml into 10 equal parts.
1
2
3
4
5
6
7
8
9
10
fig240
When 1 ml is divided into 10 equal parts, each of the parts is
1
10
1
of a ml.
10
we have 1 of the 10 equal parts.
the ml is divided into 10 equal parts.
1/ ml
10
1/ ml
10
1/ ml
10
1/ ml
10
1/ ml
10
1/ ml
10
1/ ml
10
1/ ml
10
1/ ml
10
1/ ml
10
fig241
93
1
can be written as the decimal 0.1 .
10
Therefore, the volume between each of the marks is 0.1 ml.
The fraction
0.1ml
0.1ml
0.1ml
0.1ml
0.1ml
0.1ml
0.1ml
0.1ml
0.1ml
0.1ml
fig242
This should be double-checked by counting the marks to be sure it adds up to 1 ml.
Start at zero. The volume between zero and the first mark is 0.1 ml, so the first mark is counted as 0.1
(“point one”)
0.1
fig243
94
Since the volume between each of the marks is 0.1 ml, count each mark by adding 0.1 to the number of
the mark before it.
.1
.2
.3
.4
.5
.6
.7
.8
.9
1
fig244
It does add up to 1 ml, so we have proven that each mark does indeed equal 0.1 ml or one tenth of a ml.
Another clue that we are correct is that we are counting 0.5 when we reach the ½ ml mark. 0.5 does
indeed equal ½.
.5
fig245
95
There are several syringes at your clinic that are marked the same way (with lines at tenths of a ml and ½
ml labeled). The morphine and phenobarbital Tubex syringes are marked this way, except that the
morphine syringe has a larger total volume (see below).
The 3 cc syringe is marked the same, except that it is labeled “cc” instead of “ml” and has a larger volume
(see below).
1/
2
1
11/2
2
21/2
3cc.
fig246
96
50 Unit Insulin Syringe
Insulin syringes come in two sizes, 50 units and 100 units.
5
10
10
20
15
30
20
40
25
50
30
60
35
70
40
80
45
90
50
100
units
units
fig247
The 50 unit syringe is actually a little shorter and skinnier than the 100 unit syringe (not shown by the
drawings above).
They both have an orange cap, which helps us to tell them apart from the other syringes.
The insulin syringes are different from your other syringes in two other important ways:
1. They are marked in units, not cc. Insulin is measured in units, not cc or ml or mg. (Bicillin,
Wycillin, and oxytocin are other injectable drugs in your clinic that are measured in units.)
2. The marks on the syringes show whole numbers of units, not fractions or decimals.
It is very important to understand that a mark on a 50 unit syringe indicates a different number of units
than a mark on the 100 unit syringe. Insulin is a powerful drug, and doses must be exact. A few too
many units can cause extreme low blood sugar and may result in death.
97
On this 50 unit insulin syringe, we see that the marks are numbered every 5 units (5, 10, 15, 20, and so
on) up to 50 units.
5
10
15
20
25
30
35
40
45
50
units
fig248
As with any syringe, we need to find out the volume of each unnumbered mark. If we count the marks
on the syringe, we find that there are 5 little marks from zero to 5 units.
1
2
3
4
5
5
10
fig249
98
These marks divide the 5 units into 5 equal parts.
1
2
3
4
5
5
fig250
If we divide 5 units into 5 equal parts (5 units  5), we find that each of the 5 equal parts is 1 unit
(5  5 = 1).
So, each mark on the 50 unit insulin syringe shows the volume of liquid that contains 1 unit of insulin.
1 unit
1 unit
1 unit
1 unit
1 unit
5
fig251
99
This should be double-checked by counting the marks from zero to 5 units.
1 unit
2 units
3 units
4 units
5 units
5
10
fig252
Since this counts up correctly, we know that each mark on a 50 unit insulin syringe does indeed equal 1
unit of insulin.
100
100 Unit Insulin Syringe
On the 100 unit insulin syringe below, we see that the marks are numbered every 10 units (10, 20, 30, 40,
and so on) up to 100 units.
10
20
30
40
50
60
70
80
90
100
units
fig253
As with any syringe, we need to find out the volume of each unnumbered mark. Counting the marks on
the syringe, we see that there are 5 marks from zero to 10 units.
1
2
3
4
5
10
20
fig254
101
These marks divide the 10 units into 5 equal parts.
1
2
3
4
5
10
fig255
If we divide 10 units into 5 equal parts (10 units  5), we find that each of the 5 equal parts equals 2 units
(10  5 = 2).
So, each mark on the 100 unit insulin syringe shows the volume of liquid that contains 2 units of insulin.
2 units
2 units
2 units
2 units
2 units
10
fig256
102
This should be double-checked by counting the marks from zero to 10 units by twos.
2 units
4 units
6 units
8 units
10 units
10
20
fig257
Since this counts up correctly, each mark on a 100 unit insulin syringe is for 2 units.
Sometimes we might need to give an odd number of units of insulin (1, 3, 5, 7, 9, 11, 13, and so on). On
a 50 unit syringe this would be easy, since there is a mark for every unit of insulin.
1
3
5
5
7
9
10
50 unit syringe
fig258
103
On a 100 unit syringe where only the even numbers of units are marked (2, 4, 6, 8, 10, 12, and so on), we
would have to figure out where the odd number would be.
100 unit syringe
fig259
For example, suppose we had an order for 7 units of insulin and all we had was a 100 unit insulin syringe
(it would be better to use a 50 unit syringe if we had it).
fig260
Where would 7 units be on this syringe?
104
The first step to figure this out would be to give numbers to the unnumbered marks, as we did earlier.
2
4
6
8
10
12
14
fig261
If we look at the number line below, we see that the number 7 is halfway between
6 and 8.
1
–
2
0
1
2
3
4
5
6
1
–
2
7
8
9
fig262
Therefore, on the syringe, 7 units should be halfway between 6 units and 8 units.
2
4
7 6
8
10
12
14
fig263
105
In the same way, other odd numbers of units are halfway between the even numbers that are on either side
of them.
1
3
5
7
9
11
13
2
4
6
8
12
10
20
fig264
106
Summary of Reading a Syringe
There are only a few syringes that need to be learned for Health Aide work. The key to doing syringe
dosages is to know how much each little mark is before you try to use the syringe.
This is figured out by following these three steps:
1. Count the marks from zero to 1 cc.
(On the insulin syringes, count the marks from zero to 5 units or zero to 10 units).
2. Decide if the marks are a “1” number (1 or 0.1 or 0.01 or 10) or a “2” number (0.2 or 2).
The little marks on the syringes in our village clinics are usually either a “1” number or a “2” number.
See below:
The value of the little marks on syringes:
50 unit insulin syringe
= 1 unit
3 cc syringe
= 0.1 cc
epinephrine Tubex
= 0.1 ml
1 cc TB syringe
= 0.01 cc
100 unit insulin syringe
5 cc syringe
=
=
2 units
0.2 cc
With some knowledge of decimals and fractions, we can count the little marks on a syringe or
other measuring device and figure out what amount each mark represents. This workbook shows
how to do this. Below is a brief description of how each syringe is marked:
3 cc syringe
10 marks from zero to 1 cc = 0.1 cc each.
Epinephrine Tubex 10 marks from zero to 1 ml = 0.1 ml each.
5 cc syringe
1 cc TB syringe
5 marks from zero to 1 cc = 0.2 cc each.
Tenths of a cc are labeled (.1, .2, .3, and so on)
10 marks from zero to .1 cc = 0.01 cc each.
100 unit insulin syringe
5 marks from zero to 10 units = 2 units each.
50 unit insulin syringe
10 marks from zero to 10 units = 1 unit each.
However, you are not comfortable with decimals and fractions, the simplest way to figure out the
marks on a syringe is to simply guess either a "1" number" or a "2" number and go to step 3
below:
3. Count out the little marks by ones or twos and see which choice comes out right.
Not completing this step is where most Health Aides make errors with syringes.
107
Most Health Aides have learned by experience that syringes are numbered either by ones or by twos.
Errors are made when the Health Aide does not check to see for sure which it is.
Example: If we try to count out the marks on a 3 cc syringe by twos (0.2 cc for each mark), here is
what would happen:
1/
3cc Syringe
.2
.4
.6
.8
1.0
2
1
1/
2
1
fig265
Since 1.0 does not equal ½ , we know that this is not correct. Our next try should be 0.1 cc for each
mark:
.1
.2
.3
.4
.5
.6
.7
.8
.9
1.0
1/
2
1
fig266
This comes out right. Therefore, we know that each mark is 0.1 cc.
108
Another example would be if we tried to count out the marks on a 100 unit insulin syringe by ones (1 unit
for each mark). Here is what would happen:
1
2
3
4
5
10
100 unit insulin syringe
fig267
Since 5 does not equal 10, we know that this is not correct. Our next try should be 2 units for each mark:
2
4
6
8
10
10
fig268
This adds up correctly, so we know that each mark is 2 units.
The key to safe use of a syringe (or any measuring device) is this:
 Count out the little marks before you use it to make sure they add up to the
numbers written on the syringe.
Do this every time you use a syringe. Once a medicine is injected into a patient, it can't be taken back.
Therefore, it is especially important to double-check measurements when using a syringe.
109