Nikki Grantham
Basic Terms and Conversions
within the Metric System



Most countries of the world use the Systéme
international d’unités or SI system.
The SI system is referred to as the metric
system in the United States.
Two systems of weights and measures exist
side by side in the United States today, U.S
customary system and the metric system.



The metric system is the worldwide accepted
standard measurement system.
There is only one unit of measurement for each
physical quantity.
The SI system is based on the number 10,
allowing less need for fractions.
Metric
Term
meter
Abbrev Common Comparison
Use
to Customary
m
length
kilogram
kg
mass
liter
L
volume
a little more
than a yard
about 2.2
pounds
a little more
than a quart
Prefix
kilo
hecto
deka
Symbol
k
h
da
deci
centi
milli
d
c
m
Meaning
1000  base unit
100  base unit
10  base unit
base unit
1/10 of base unit
1/100 of base unit
1/1000 of base unit


To change from a smaller unit to a larger unit
move the decimal point in the original quantity
one place to the left for each larger unit of
measure until you obtain the desired unit of
measure.
To change from a larger unit to a smaller unit,
move the decimal point in the original quantity
one place to the right for each smaller unit of
measure until you obtain the desired unit of
measure.
Measure
of length
kilometer
hectometer
dekameter
Symbol
km
hm
dam
100 m
10 m
Number of 1000 m
meters
Measure
of length
meter decimeter centimeter millimeter
Symbol
m
Number 1 m
of meters
dm
cm
mm
0.1 m
0.01 m
0.001 m
Convert 54.6 m to km.

Convert 15 L to mL.

Convert 0.89 kg to cg.
Solutions:

Meters is a smaller unit than km. Move the
decimal 3 places to the left, 0.0546 km.

Liter is a larger unit than milliliter. Move the
decimal point 3 places to the right, 15,000 mL.

Kilogram is a larger unit than centigram.
Move the decimal point 5 places to the right
0.89 kg = 89,000 cg

A case of fruit juice contains twenty-four 0.75
liter bottles. How many 250 milliliter glasses
can you fill using one case of juice?
Solution: The case of juice contains
24(0.75) = 18 L.
Converting 18 L = 18,000 mL. If each glass hold
250 mL,
18,000
=
72
then250
glasses can be filled.
a.
351,000 dm
b.
35,100 dm
c.
351 dm
d.
35.1 dm
a.
351,000 dm
b.
35,100 dm
c.
351 dm
d.
35.1 dm
a.
0.1 times greater
b.
10 times greater
c.
100 times greater
d.
1000 times greater
a.
0.1 times greater
b.
10 times greater
c.
100 times greater
d.
1000 times greater
Length, Area, and Volume


The meter is used to measure things that we
normally measure in yards and feet.
Centimeters and millimeters are used to measure
what we normally measure in inches.
 A centimeter is a little less than a half of an
inch.
 A millimeter is about the thickness of a dime.
Example: The length of a pair of scissors would
be measured in centimeters.
Areas are always expressed in square units.
Example:
The length of a rectangular park is 82.5 m, and its
width is 25.4 m. Find the area of the park.

Solution: Area = length  width.
A=82.5m x 25.4 m
A=2095.5m2



When a figure has three dimensions: length, width
and height, the volume can be found.
The volume of an item can be considered the space
occupied by the item.
Volume can be expressed in terms of liters or cubic
meters.
Volume in Cubic Units
1 cm3
1 dm3
1 m3
=
=
=
Volume in Liters
1 mL
1L
1 kL

When the volume of a liquid is measured, the
abbreviation cc is often used instead of cm3 to
represent cubic centimeters.
Example: An asthma patient must mix 0.25 cc of a
bronchodilator with 2 cc of saline to use in an
aerosol machine.

How many milliliters of the bronchodilator
will be administered?

What is the total volume of drug and saline
solution in milliliters?
Example:
An asthma patient must mix 0.25 cc of a bronchodilator
with 2 cc of saline to use in an aerosol machine.

How many milliliters of the bronchodilator will be
administered?

What is the total volume of drug and saline solution in
milliliters?
Solution:

Since 1 cc is equal in volume to 1 milliliter, there will
be 0.25 milliliters of the bronchodilator.

The total volume is 0.25 + 2 or 2.25 cc, which is equal
to 2.25 mL.
A cylindrical shampoo bottle has a diameter of
6 cm and a height of 12 cm. What is the volume
in milliliters?
Solution:
V   r 2h

2
V  3.14 3 12
V  339.12 cm3
V  339.12 mL
Mass and Temperature

Although weight and mass are not the same,
on Earth they are proportional to each other.
 Mass is a measure of the amount of matter in
an object.
 Weight is the measure of gravitational pull on
an object.




The kilogram is the basic unit of mass in the
metric system.
 Example: A man has the mass of about 75 kg.
The gram is relatively small and used in place of
the ounce.
 Example: A nickel has the mass of about 5 g.
The milligram is used in the medical and scientific
fields.
The metric tonne (t) is used to express mass of
heavy items. One metric tonne = 1000 kg.
Determine which metric unit you would use to
express the mass of the following.
a) A spider
c) A bicycle
b) A nickel
d) A box of cereal
Determine which metric unit you would use to
express the mass of the following.
a) A spider
c) A bicycle
b) A nickel
d) A box of cereal
Solution:
a) Milligrams
b) Grams
c) Kilograms
d) Grams
Volume in
Volume in
Cubic Units
Liters
1 cm3
=
1 mL
=
1 dm3
1 m3
=
=
1 L
1 kL
Mass of
Water
1g
=
1 kg
= 1 t (1000 kg)
A fish tank is 1 m long, 60 cm high and 260 mm wide.
Question:
Determine the number of liters that the tank holds.
Solution:
V=l x w x h
(Volume = length x width x height)

V = 1m x 0.26m x 0.6m

V = 0.156 m3
Since 1 m3 of water = 1 kL of water,
0.156 m3 = 0.156 kL, or 156 liters of water
A fish tank is 1 m long, 60 cm high and 260 mm
wide.
Question:
What is the mass of the water in kilograms?

Solution:

Since 1L = 1 kg, 156 L = 156 kg of water.

The term degrees Celsius (ºC) is used to
measure temperature.
Temperature
ºC
ºF
0ºC
32ºF
22ºC
71.6ºF
Description
Water freezes
37ºC
100ºC
Body temperature
Water boils
98.6ºF
212ºF
Comfortable room
temperature



The temperature of a can of
frozen juice is about 2 __.
The temperature of a person
with a fever is about 101.5 __.
The temperature of a bowl of
hot soup is about 175 __.
Solution:
a) ºC
b) ºF
c) ºF

To covert from
Celsius to Fahrenheit
use the following
formula.
9
F  C  32
5

To covert from
Fahrenheit to Celsius
use the following
formula.

5
C  F  32
9

The air temperature on a warm summer day is
about 85ºF. What is the equivalent temperature on
the Celsius thermometer?


9
Solution: C  5 F  32


5
C  85  32
9
5
C  53
9
C  29.4

 

The equivalent temperature is about 29.4ºC.
The temperature of a
cold glass of milk is
about 5ºC . What is
the equivalent
temperature on the
Fahrenheit
thermometer?

Solution:
9
F  C  32
5
9
F  5  32
5
F  9  32
F  41

The equivalent temperature
is about 41ºF.
a.
80º C
b.
20º C
c.
140º C
d.
Can’t determine.
a.
80º C
b.
20º C
c.
140º C
d.
Can’t determine.
Dimensional Analysis and
Conversions to and from the
Metric System



Dimensional analysis is a procedure used to
convert from one unit of measurement to a
different unit of measurement.
A unit fraction is any fraction in which the
numerator and denominator contain different
units and the value of the fraction is 1.
Examples of unit fractions:
16 oz
1 lb
1 hr
60 min
12 in.
1 ft
U.S. Customary Units
1 foot = 12 inches
1 quart = 2 pints
1 yard = 3 feet
1 gallon = 4 quarts
1 mile = 5280 feet
1 minute = 60 seconds
1 pound = 16 ounces
1 hour = 60 minutes
1 ton = 2000 pounds
1 day = 24 hours
1 cup (liquid) = 8 fluid ounces
1 year = 365 days
1 pint = 2 cups
A recipe calls for 8 cups of blueberries. How
many pints is this?
Solution:
 1 pint 
8 cups = 8 cups 
 4 pint s

 2 cups 



Convert 75 miles per hour to inches per minute.
Solution:
mi  mi   5280ft   12 in   1 hr 
75   75  
hr  hr   1 mi   1 ft   60 min 

75 5280 12 in


60
in
= 79,200
min
min
LENGTH
U.S. to Metric
1 inch (in.) ≈ 2.54 centimeters (cm)
1 foot (ft) ≈ 30 centimeters (cm)
1 yard (yd) ≈ 0.9 meter (m)
1 mile (mi) ≈ 1.6 kilometers (km)
AREA
U.S. to Metric
1 square inch (in.2) ≈ 6.5 square centimeters
(cm2)
1 square foot (ft2) ≈ 0.09 square meter (m2)
1 square yard (yd2) ≈ 0.8 square meter (m2)
1 square mile (mi2) ≈ 2.6 square kilometers
(km2)
1 acre ≈ 0.4 hectare (ha)
VOLUME
U.S. to Metric
1 teaspoon (tsp) ≈ 5 milliliters (ml)
1 tablespoon (tbsp) ≈ 15 milliliters (ml)
1 fluid ounce (fl oz) ≈ 30 milliliters (ml)
1 cup (c) ≈ 0.24 liter (l)
1 pint (pt) ≈ 0.47 liter (l)
VOLUME
U.S. to Metric
1 quart (qt) ≈ 0.95 liter (l)
1 gallon (gal) ≈ 3.8 liters (l)
1 cubic foot (ft3) ≈ 0.03 cubic meter (m3)
1 cubic yard (yd3) ≈ 0.76 cubic meter (m3)
WEIGHT OR MASS
U.S. to Metric
1 ounce (oz) ≈ 28 grams (g)
1 pound (lb) ≈ 0.45 kilogram (kg)
1 ton (T) ≈ 0.9 tonne (t)
A gas tank holds 22.6 gallons of gas. How
many liters is this?
Solution:
3.8
22.6 gal ´
= 85.88 l
gal

The area of a box is 14.25 in2. What is its area in
square centimeters?
Solution:

2


6.5
cm
2
2
14.25 in 

92.625
cm
 1 in2 
A road in Toronto, Canada shows that the
speed limit is 62 kph. Determine the speed in
miles per hour.
Solution:
 1 mi  62
62 km 

mi  38.75 mi

 1.6 km  1.6

Since 62 km equals 38.75 mi, 62 kph is
equivalent to 38.75 mph.
A newborn baby weighs 8 pounds 4 ounces. If
20 mg of a medication is given for each
kilogram of the baby’s weight, what dosage
should be given?
Solution: 
16 oz 
8 lbs 
 4 oz  128 oz  4 oz  132 oz

 1 lb 
 28 g   1 kg   20 mg 
132 oz 
 73.92 mg





 oz   1000 g   1 kg 
The dosage of the medication is 73.92 mg.
a.
3000 cm2
b.
50 m2
c.
300 m2
d.
Can’t determine.
a.
3000 cm2
b.
50 m2
c.
300 m2
d.
Can’t determine.
a.
1000 times greater
b.
10,000 times greater
c.
100,000 times greater
d.
1,000,000 times greater
a.
1000 times greater
b.
10,000 times greater
c.
100,000 times greater
d.
1,000,000 times greater
a.
1000 times greater
b.
10,000 times greater
c.
100,000 times greater
d.
1,000,000 times greater
a.
1000 times greater
b.
10,000 times greater
c.
100,000 times greater
d.
1,000,000 times greater
a.
15.2 l
b.
1.052 l
c.
4l
d.
16 l
a.
15.2 l
b.
1.052 l
c.
4l
d.
16 l
a.
7.5 km
b.
19.2 km
c.
24 km
d.
60 km
a.
7.5 km
b.
19.2 km
c.
24 km
d.
60 km
a.
84.44º C
b.
48.89º C
c.
248º C
d.
273.6º C
a.
84.44º C
b.
48.89º C
c.
248º C
d.
273.6º C
a.
35º F
b.
70.56º F
c.
228.6º F
d.
203º F
a.
35º F
b.
70.56º F
c.
228.6º F
d.
203º F