MODULE A - 4
MEASUREMENT SYSTEMS &
SCIENTIFIC NOTATION
OBJECTIVES
•
At the end of this module, the student will be
able to…
 Identify and compare the systems of
measurement used in the clinical setting.
 Identify the standard prefixes used in the metric
system
 State the metric units of length, mass, volume,
time, and temperature.
 Distinguish between the metric units for liquid
(mL) and solid volume (cc) measurements.
Measurement systems
•
Method of quantifying matter
 Solids, liquids & gases
•
Quantities include:
 Length
 Area
 Weight
 Volume
 Pressure
 Temperature
 Time
•
Systems used in medicine:
A. Conventional
B. Metric
C. Standard International
Conventional Systems
• Also known as:
 British
 English
 U.S Customary
 (FPS) foot, pound, second
• Commonly used in U.S.
FPS
Examples of length & area
12 inches
=
1 foot
3 feet (36 inches)
=
1 yard
220 yards
=
1 furlong
8 furlongs
=
1 mile
1,760 yards
=
1 mile
5,280 feet
=
1 mile
1 sq. foot (foot2)
=
122 sq. inches
1 sq. yard (yard2)
=
9 sq. feet
43,560 sq. feet
=
1 acre
1 sq. mile (mile2)
=
640 acres
Examples of liquid measure
1 teaspoon (tsp)
=
1/
3
2 tablespoon (tbsp)
=
1 fluid ounce
1 fluid ounce (oz)
=
1/
8
cup
2 fluid ounces
=
1/
4
cup
2 2/3 fluid ounces
=
1/
3
cup
4 fluid ounces
=
1/
2
cup
5 1/3 fluid ounces
=
2/
3
cup
6 fluid ounces
=
3/
4
cup
8 fluid ounces
=
1 cup
2 cups (c)
=
1 pint
2 liquid pints (pt)
=
1 liquid quart (qt)
4 liquid pints
=
1 gallon (gal)
tablespoon
Examples of dry measure
1 dry quart
=
2 dry pints
8 dry pints
=
1 peck
4 pecks
=
1 bushel
Standard International (SI)
• Simplified modification of metric system.
• Worldwide effort started in 1960s to standardize
to this system.
• Also known as:
 (MKS) meter, kilogram, second
MKS
Comparison
Conventional Units
Standard International
Units
Length
inch or foot
meter
Volume
Fluid ounce
Liter
Cubic Foot (ft3)
Area
in2 or ft2
m2
Metric System
• Developed in Europe.
• Has all units based on multiples of 10.
• Also known as:
 (CGS) centimeter, gram, second
CGS
Measurements in Respiratory Therapy
• Length
 Meter (m)
• Volume
 Liter (L)
• Mass
 Gram (g)
• Time
 Seconds (sec)
• Temperature
 Centigrade (Celsius), Kelvin, Fahrenheit
• Pressure
 Centimeters of Water (cm H2O), Pounds per square
inch (psi), Millimeters of mercury (mm Hg), Torr,
Pascal (Pa), and Atmospheres (atm)
• Force
 Dynes
Conversion
• Conversion within the metric system is easy
 Everything based on multiples of ten.
• Conversion from one system to the other:
 Must know the conversion factors.
Conversion
• Conversion within these systems or from one
system to the other:
 You Must know how to do metric conversions.
 I will provide the S.I. and conventional factors on
an exam or quiz.
• There are too many to memorize.
• Gimli Glider & Mars Climate Orbiter
Basic (fundamental) Units
• Basic unit has value of one. (1x100 = 1)
 One Liter
• Smaller - milliliter
• Larger - kiloliter
 One Gram
• Smaller – microgram
• Larger - hectogram
Larger
 One Meter
• Smaller - decimeter
• Larger - Megameter
Smaller
Opposite of the number line
Metric Chart
Basic or Fundamental Unit
Liter
Gram
Meter
105
104
103
102 101
100
10-1 10-2
10-3 10-4 10-5
|-------|-------|-------|-------|-------|-------|-------|-------|------|-------|
kilo
hecto deca
x1000 x100 x10
(k)
(h)
(da)
LARGER
deci centi milli
1  1
1


10
100 1000
(d)
(c) (m)
SMALLER
Greek Prefixes - Units to the left
of the basic unit and larger.
• BASIC UNIT = One Liter, Gram or Meter
•
•
•
•
•
•
•
•
•
10 1
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
deca (da)
hecto (h)
kilo (k)
10 x larger
100 x larger
1000 x larger
10
100
1000
Mega (M)
1,000,000x
1,000,000
Giga (G)
1,000,000,000x
1,000,000,000
Latin Prefixes Units to the right
of the basic unit and smaller.
• BASIC UNIT = One Liter, Gram or Meter
•
10 -1 deci (d); 10 x smaller; 1/10; x 0.1
•
10 -2 centi (c); 100 x smaller; 1/100; x 0.01
•
10 -3 milli (m); 1000 x smaller; 1/1,000; x 0.001
•
10 -4
•
10 -5
•
10 -6 micro (m) or (mc); 1,000,000 x smaller; 1/1,000,000; x 0.000001
•
10 -7
•
10 -8
•
10 -9 nano (n); 1,000,000,000 x smaller; 1/1,000,000,000; x 0.000000001
•
10-10 Angstrom (Å); 10,000,000,000 x smaller; 1/10,000,000,000; x 0.0000000001
Scientific Notation
• A method of expressing the value of a very small or very
large number.
• Scientific Notation: (base exponent)
 Base is the number to be multiplied by itself (usually
10).
 Exponent is the number of times it is multiplied.
• 103 = 10 x 10 x 10 = 1,000
Scientific Notation
 Example:
• A kilometer is 1,000 times larger than a meter
• Count the zeros (that equals exponent)
• 103
• 10x10x10 times larger
Scientific Notation
 Example:
• Angstrom (Å) is 10 billion times smaller than a meter
(m)
• That is…10,000,000,000 times smaller
• Count the zeros to determine exponent
10
10
or
1
1010
or
1
10,000,000,000
• Can also be written as 0.0000000001
• 10x10x10x10x10x10x10x10x10x10 times smaller
Numbers and Exponents
100=
1
a x 100 = a
101=
10
a x 101 = a x 10
102=
100
a x 102 = a x 100
103=
1000
a x 103 = a x 1000
106=
1,000,000
a x 106 = a x 1,000,000
109=
1,000,000,000
a x 109 = a x 1,000,000,000
10-1
=
0.1
a x 10-1 = a x 0.1
10-2
=
0.01
a x 10-2 = a x 0.01
10-3
=
0.001
a x 10-3 = a x 0.001
10-6
=
0.000001
a x 10-6 = a x 0.000001
10-9
=
0.000000001
a x 10-9 = a x 0.000000001
Numbers and Exponents
Positive exponent = # of zeros
5 x 100 =
5
5 x 101 =
50
5 x 102 =
500
5 x 103 =
5000
5 x 106 =
5,000,000
5 x 109 =
5,000,000,000
Negative exponent = # of decimal places
5 x 10-1 =
0.5
5 x 10-2 =
0.05
5 x 10-3 =
0.005
5 x 10-6 =
0.000005
5 x 10-9 =
0.000000005
Examples - Avogadro’s Number
Expresses the number of atoms in one mole of a
gas
Long form:
602,000,000,000,000,000,000,000 atoms
Scientific notation:
6.02 x 10 23 atoms
Process: Count over to the left, the number of decimal places
to get a number between 1 & 10
Example - Mass of an electron
Long Form:
0.000 000 000 000 000 000 000 000 000 000 911 grams
Scientific Notation:
9.11 x 10-31 grams
Process: Count over to the right the number of decimal places
necessary to get a number between 1 and 10
Practice:
Express the following exponentially
• 500
=
5 x 102
(count over to left 2 decimal places)
• 93,000,000
=
_________________
• 0.0003
=
_________________
• 0.000000024
=
_________________
Exponent Relationship to Basic Unit
• Negative exponents are smaller (10 –3)
• Positive exponents are larger (10 3)
If the metric system was money…
|
|
|
|
$1,000.00 $100.00 $10.00 $1.00
Basic
Unit
|
|
10 cent
1cent
0.10
0.01
One more point
regarding units of
measure.
Why is mL and cc (cm3) the same?
•
Cubic centimeter (cc or cm3) and millimeter (mL)
are used interchangeably in medicine.
 The unit cc is a length measurement.
 The unit mL is a volume measure.
•
A cube 1 cm long x 1 cm wide by 1 cm high (l x w x
h = area) will hold 1 mL of liquid volume.
•
We therefore use the units interchangeably.
 1 cc or cm3 = 1 mL
The volume of this cube
1 cm deep
Cubic
centimeter
1 cm length
is one mL.
1 cm high
1 mL = 1 cc = 1 cm3
Additional Conversion Factors
Length:
1 meter
=
39.37 inches
1 cm
=
.3937 inches
1 km
=
0.62 miles
Volume:
1 mL =
1 cc
=
1L
=
1.0567 qts.
946 mL
=
1 qt.
1 pint
=
473 mL
1 kg
=
2.2 pounds (lbs)
1 lb
=
454 grams
1 cm3