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8.1 Basic Terms & Conversions in the Metric System
Basic Units of Measurement:
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•Kilogram (kg) used to measure mass. A little more than 2 pounds.
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•Liter (l) used to measure volume. A little more than a quart.
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The metric system is based on powers of 10 (the decimal system).
Prefix
kilo
hecto
deka
———
deci
centi
milli
Symbol
k
h
da
———
d
c
m
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Meaning
1000 x base unit
100 x base unit
10 x base unit
base unit
1/10 x base unit
1/100 x base unit
1/1000 x base unit
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•Meter (m) used to measure length. A little longer than a yard.
•Celsius (°C) used to measure temperature.
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Changing Units within the Metric System
1. To change from a smaller unit to a larger unit, move the
decimal point in the original quantity one place to the
for each larger unit of measurement until you obtain the
desired unit of measurement.
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2. To change form a larger unit to a smaller unit, move the
decimal point in the original quantity one place to the
for each smaller unit of measurement until you obtain the
desired unit of measurement.
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k
h
(larger)
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d
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m
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(smaller)
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Example Convert the given unit to the unit indicated.
#42
7 dam = ________ m
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#46
1.34 ml = ________ l
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#54
24 dm = ________ km
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Example Arrange the quantities in order from smallest to
largest.
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#60
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5.1 dam
0.47 km
590 cm
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8.2 Length, Area, and Volume
Length
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Recall the meter is a little longer than a yard. It is used to
measure things that we normally measure in feet or yards.
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A kilometer is about 0.6 mile. It is used to measure things we
normally measure in miles.
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A centimeter is a little less than ½ inch.It is about the width of
your little finger. A millimeter is about the thickness of a dime.
These are used to measure things we normally measure in
inches.
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0 1 2 3 4 5 6 7 8 9 10
0
1
2
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centimeters
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inches
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Example Indicate the metric unit of measurement that you would
use to express the following.
#26 The length of a jump rope
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#28 The length of a paper clip
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#32 The diameter of a jump rope
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#36 The distance to the moon
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Area
Used to measure two dimensional figures. The area of a figure is
measured in
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Area = (1 m)(1 m) = 1 m2
1m
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1m
Square centimeters are used where we normally use square
inches. Square meters replace square feet or square yards.
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To measure large land areas, the metric system uses a square
unit 100 meters on each side (a hectare). A hectare is about
2.5 acres.
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Very large areas are measured in square kilometers.
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Example Indicate the metric unit of measurement that you would
use to express the following.
#62 The floor of your classroom
#66
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Washington, D.C.
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A piece of notebook paper
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Volume
Used to measure three dimensional figures. The volume of a figure
is measured in
1m
1m
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Volume = (1 m)(1 m)(1 m) = 1 m3
1m
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Cubic meters are generally used to express the volume of large
amounts of solid material.
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The volume of liquids is generally expressed in liters. A liter is a
little larger than a quart. Liters are used in place of pints, quarts,
and gallons.
Milliliters are used to express the volume of very small amounts of
liquid. Kiloliters are used to express very large amounts of liquid.
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A liter is defined as the volume of a cubic decimeter.
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1 liter = (1 dm)(1 dm)(1 dm)
1 dm
1 dm
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1
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Recall 1 dm = 10 cm, so
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1 liter = (10 cm)(10 cm)(10 cm)
1 dm
= 1000 cm3 [cm3 is sometimes
abbreviated cc]
Also, since 1 l = 1000 ml, we have
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1ml = 1 cm3
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In summary,
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1000 ml = 1000 cm3
or
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Volume in
cubic units
cm3
=
1 ml
1 dm3
1 m3
=
=
1l
1 kl
1
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Volume in
liters
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Example Indicate the metric unit of measurement that you would
use to express the following.
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#84 Water in a hot-water heater
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#86 Air in a basketball
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#90 Asphalt needed to pave a driveway
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Example #112 A rectangular fish tank is 70 cm long, 40 cm
wide, and 20 cm high.
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(a) How many cubic centimeters of water will the tank hold?
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(b) How many milliliters of water will the tank hold?
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(c) How many liters of water will the tank hold?
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8.3 Mass and Temperature
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Mass
Weight is a measure of the earth's gravitational pull.
is
the measure of the amount of matter (atoms and molecules) that
objects are made of. In space, the mass of an object does not
change, but its weight does. On earth the mass of an object is
proportional to the weight of the object. For this course we can
treat weight and mass as the same thing.
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The kilogram is the basic unit of mass. It is a little more than
2 pounds. It is used to measure things we normally measure in
pounds.
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The gram is used to measure things we normally measure in
ounces. A large paper clip has the mass of about 1 g.
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The milligram is used to measure extremely small quantities.
It is used primarily in medical and scientific fields.
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The metric tonne (t) is used to express the mass of heavy
items. It is a little more than a ton (2000 pounds).
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Example Indicate the metric unit of measurement that you would
use to express the following.
#12 A box of cereal
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#14 A Cadillac
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#16 A mosquito
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In the metric system we have the following relationships:
Volume in
cubic units
Volume
in liters
1 ml
1 cm3
=
1 dm3
=
1l
1 m3
=
1 kl
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Mass of
water
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=
1g
=
1 kg
= 1 t (1000kg)
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These relationships allow conversions between mass and
volume. Try to convert your weight, in pounds, to gallons!
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Temperature
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Celsius (°C) used to measure temperature.
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212°F = 100°C (water boils)
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98.6°F = 37 °C (body temp.)
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32°F = 0°C (water freezes)
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To convert between Celsius and Fahrenheit we use the following
formulas:
Celsius to Fahrenheit:
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Fahrenheit to Celsius:
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Example Convert each temperature as indicated.
#38
-5°C = _______°F
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#46
75°F = _______°C
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8.4 Dimensional Analysis
Dimensional Analysis is a procedure that allows us to convert
from one unit of measurement to a different unit of measurement.
For example, if it takes you 5 minutes to run a race, we can
determine how many seconds it takes:
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Dimensional analysis can be used to convert between our customary
measurement system and the metric system.
Conversion Factors: p. 419 Table 8.7
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#14 160 kg to pounds
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Some conversions may require more than one unit fraction.
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Example How many seconds are in one year?
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Example Convert the quantity to the indicated units.
#10 9 lb to kilograms
2
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60 sec
5 min ×
= 300 sec
1 min
is any fraction in which
numerator and denominator contain different units and
the value of the fraction is 1.
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Example Convert the quantity to the indicated units.
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#16 765 mm to inches
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Example #46 Yosemite National Park has an
area of 1189 mi2. What is its area in square
kilometers?
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