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SEVENTH EDITION and EXPANDED SEVENTH EDITION
Slide 8-1
Chapter 8
The Metric System
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8.1
Basic Terms and Conversions
within the Metric System
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SI System and U.S. Customary System
„
„
„
Most countries of the world use the 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.
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Slide 8-4
Advantages to Using 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.
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Slide 8-5
Basic Terms
Metric
Term
Abbrev.
Common Use
Comparison to
Customary
meter
m
length
a little more than
a yard.
kilogram
kg
mass
about 2.2
pounds
liter
L
volume
a little more than
a quart
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Slide 8-6
Metric Prefixes
Prefix
Symbol
Meaning
kilo
k
1000 × base unit
hecto
h
100 × base unit
deka
da
10 × base unit
base unit
deci
d
1
10
of base unit
centi
c
of base unit
milli
m
1
100
1
1000
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of base unit
Slide 8-7
Changing Units within the Metric
System
„
„
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 measurement until
you obtain the desired unit of measure.
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Slide 8-8
Example: Changing Units
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.
„
Liter is a larger unit than milliliter. Move the decimal
point 3 places to the right, 15,000.
„
0.89 kg = 89,000 cg
„
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Slide 8-9
Example: Application
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,
then 18,000 = 72 glasses can be filled.
250
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Slide 8-10
8.2
Length, Area, and Volume
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Length
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„
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.
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Slide 8-12
Area
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 = 82.5 × 25.4
A = 2095.5 m2
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Slide 8-13
Volume
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„
„
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
Volume in Liters
1 cm3
=
1 mL
1 dm3
=
1L
1 m3
=
1 kL
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Slide 8-14
Volume
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?
„
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Slide 8-15
Volume continued
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.
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Slide 8-16
Example: Volume Application
A cylindrical shampoo bottle has a diameter of
6 cm and a height of 12 cm. What is the volume
in milliliters?
Solution:
2
V = πr h
V = 3.14 ( 3 ) 12
2
V = 339.12 cm
3
V = 339.12 mL
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Slide 8-17
8.3
Mass and Temperature
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Mass
„
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.
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Slide 8-19
Metric System
„
The kilogram is the basic unit of mass in the metric
system.
‰
„
The gram is relatively small and used in place of the
ounce.
‰
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„
Example: A man has the mass of about 75 kg.
Example: A nickel has the mass of about 5 g.
The milligram is used in the medical and scientific fields.
The metric tonne is used to express mass of heavy
items. One metric tonne = 1000 kg.
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Slide 8-20
Example: Choosing an Appropriate
Unit
a)
b)
Determine which metric unit you would use to express
the mass of the following.
A spider
c)
A bicycle
A nickel
d)
A nickel
Solution:
a) Milligrams
b) Grams
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c)
d)
Kilograms
Grams
Slide 8-21
Volume and Mass of Water
Volume in
Cubic Units
=
1 cm3
Volume in
Liters
1 mL
Mass of Water
=
1g
1 dm3
=
1 L
=
1 kg
1 m3
=
1 kL
=
1 t (1000 kg)
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Slide 8-22
Example: Capacity
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„
A fish tank is 1 m long, 60 cm high and 260
mm wide.
Determine the number of liters that the tank
holds.
What is the mass of the water in kilograms.
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Slide 8-23
Example: Capacity continued
Solution:
„
V = l ×w × h
= 1× 0.26 × 0.6
= 0.156 m3
„
Since 1 m3 of water = 1 kL of water,
0.156 m3 = 0.156 kL, or 156 liters of water
Since 1L = 1 kg, 156 L = 156 kg of water.
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Slide 8-24
Temperature
„
The term degrees Celsius
temperature.
( C ) is used to measure
o
Temperature
o
o
C
o
0C
o
F
Description
o
32 F
o
Water freezes
22 C
71.6 F
Comfortable room
37 o C
98.6 o F
Body temperature
100 o C
212 F
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o
Water boils
Slide 8-25
Example:
Choose o
F
or
o
C.
The temperature of a
can of frozen juice
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) o C.
b) o F
c) o F
„
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Slide 8-26
Conversions
„
To covert from Celsius to
Fahrenheit use the
following formula.
9
F = C + 32
5
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„
To covert from
Fahrenheit to Celsius use
the following formula.
5
C = (F − 32 )
9
Slide 8-27
Example: Conversions
The air temperature on a
warm summer day is
o
about 85 F. What is the
equivalent temperature
on the Celsius
thermometer?
„
5
C = (F − 32 )
9
5
C = ( 85 − 32 )
9
5
C = ( 53 )
9
C ≈ 29.4
„
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Solution:
The equivalent temperature is
o
about 29.4 C.
Slide 8-28
Example: Conversions
The temperature of a
cold glass of milk is
o
about 5 C . 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
„
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The equivalent temperature is
about
o
41 F .
Slide 8-29
8.4
Dimensional Analysis and
Conversions to and from the
Metric System
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Dimensional Analysis
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„
„
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
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1 hr
60 min
12 in.
1 ft
Slide 8-31
U.S. Customary Units
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
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Slide 8-32
Example: Using Dimensional Analysis
A recipe calls for 8 cups of blueberries. How many
pints is this?
⎛ 1 pint ⎞
Solution:
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 )( 5280 )(12 ) in
75
= ⎜ 75 ⎟⎜
=
⎟
⎜
⎟
⎜
⎟
hr ⎝ hr ⎠⎝ 1 mi ⎠ ⎝ 1 ft ⎠ ⎝ 60 min ⎠
60
min
in
= 79,200
min
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Slide 8-33
Conversion to
and from the
Metric System
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Slide 8-34
Example: Volume and Area
A gas tank holds 22.6 gallons of gas. How many liters
is this?
3.8 L
22.6 gal =
= 85.88 L
Solution:
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
⎟
2
⎝ 1 in ⎠
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Slide 8-35
Example: Converting Speed
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 kpm is equivalent to
38.75 mph.
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Slide 8-36
Example: Weight (Mass) Conversion
for Medication
A newborn baby weighs 8 pounds 4 ounces. If 20 mg of
a medication is given for each kilogram of the babies
weight, what dosage should be given?.
Solution:
⎛ 16 oz ⎞
= 128 oz + 4 oz = 132 oz
8 lbs ⎜
⎟
⎝ 1 lb ⎠
⎛ 20 mg ⎞
⎛ 28 g ⎞ ⎛ 1 kg ⎞
132 oz ⎜
⎜
⎟ = 3.696 kg ⎜
⎟ = 73.92 mg
⎟
⎝ oz ⎠ ⎝ 1000 g ⎠
⎝ 1 kg ⎠
The dosage of the medication is 73.92 mg.
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Slide 8-37