The Metric System
Christopher G. Hamaker, Illinois State University, Normal IL
© 2005, Prentice Hall
The Metric System
• The English System was used primarily in the
British Empire and wasn’t very standardized.
• The French organized a committee to devise a
universal measuring system.
• After about 10 years, the committee designed and
agreed on the metric system.
• The metric system offers simplicity with a single
base unit for each measurement.
Metric Base Units
Basic Units in the Metric System
Physical Quantity
Basic Unit
Symbol
Length
meter
m
Mass
gram
g
Volume
liter
L
Time
Energy
Amount of Matter
Second
Joule
Mole
S
J
mol
Unit Definitions
• A meter was defined as 1/10,000,000 of the
distance from the North Pole to the equator.
• A kilogram (1000 grams) was equal to the mass of
a cube of water measuring 0.1 m on each side.
• A liter was set equal to the volume of one
kilogram of water at 4C.
Metric System Advantage
• Another advantage of the metric system is that it
is a decimal system.
• It uses prefixes to enlarge or reduce the basic
units.
• For example:
– A kilometer is 1000 meters.
– A centimeter is 1/100 of a meter.
Metric System Prefixes
• The following table lists the common prefixes
used in the metric system:
Metric Prefixes Continued
• For example, the prefix kilo- increases a base unit
by 1000:
– 1 kilogram is 1000 grams.
• The prefix centi- decreases a base unit by a factor
of 100:
– 1 centimeter is 0.01 meters.
Metric Symbols
• The names of metric units are abbreviated using
symbols. Use the prefix symbol followed by the
symbol for the base unit, so:
– kilometer is abbreviated km.
– milligram is abbreviated mg.
– microliter is abbreviated mL.
– nanosecond is abbreviated ns.
Metric Equivalents
• We can write unit equations for the conversion
between different metric units.
• The prefix kilo- means 1000 basic units, so 1
kilometer is 1000 meters.
• The unit equation is 1 km = 1000m.
• Similarly, a centimeter is 1/100 of a meter, so the
unit equation is 1 cm = 0.01 m.
Temperature
• Temperature is a measure of the average kinetic
energy of the individual particles in a sample.
• There are three temperature scales:
– Celsius
– Fahrenheit
– Kelvin
• Kelvin is the absolute temperature scale.
Temperature Scales
• On the Fahrenheit scale, water freezes at 32°F
and boils at 212°F.
• On the Celsius scale, water freezes at 0°C and
boils at 100°C. These are the reference points for
the Celsius scale.
• Water freezes at
273K and boils at
373K on the Kelvin
scale.
Temperature Conversions
• This is the equation for converting °C to °F.
°C ×
(
180°F
100°C
)
= °F
• This is the equation for converting °F to °C.
(
)
100°C
= °C
(°F - 32°F) × 180°F
• To convert from °C to K, add 273.
°C + 273 = K
Fahrenheit-Celsius Conversions
• Body temperature is 98.6°F. What is body
temperature in Celsius?
(98.6°F - 32°F) ×
(
100°C
180°F
)
= 37.0°C
Heat
• Heat is the flow of energy from an object of
higher temperature to an object of lower
temperature.
• Heat measures the total energy of a system while
temperature measures the average energy of
particles in a system.
• Heat is often expressed in terms of joules (J) or
calories (cal).
Volume by Calculation
• The volume of an object is calculated by
multiplying the length (l) by the width (w) by the
thickness (t).
volume = l × w × t
• All three measurements must be in the same units.
• If an object measures 3 cm by 2 cm by 1 cm, the
volume is 6 cm3 (cm3 is cubic centimeters).
Cubic Volume vs. Liquid Volume
• The liter (L) is the basic unit of volume in the
metric system.
• One liter is
defined as the
volume
occupied by a
cube that is 10
cm on each side.
Cubic & Liquid Volume Units
• 1 liter is equal to 1000 cubic centimeters
– 10 cm × 10 cm × 10 cm = 1000 cm3
• 1000 cm3 = 1 L = 1000 mL.
• Therefore, 1 cm3 = 1 mL.
Volume by Displacement
• If a solid has an irregular shape, its volume cannot
be determined by measuring its dimensions.
• You can determine its volume indirectly by
measuring the amount of water it displaces.
• This technique is call volume by displacement.
Volume by Displacement
• You want to measure the volume of an irregularly
shaped piece of jade.
• Partially fill a volumetric flask with water and
measure the volume of the water.
• Add the jade, and
measure the
difference in volume.
• The volume of the
jade is 10.5 mL.
The Density Concept
• The density of an object is a measure of its
concentration of mass
• Density is defined as the mass of an object
divided by the volume of the object.
mass
= density
volume
Density
• Density is expressed in different units. It is
usually grams per milliliter (g/mL) for liquids,
grams per cubic centimeter (g/cm3) for solids, and
grams per liter (g/L) for gases.
Estimating Density
• We can estimate the density of a
substance by comparing it to
another object.
• A solid object will float on top a
liquid with a higher density.
• Object S1 has a density less than
that of water, but larger than that of
L1.
• Object S2 has a density less than
that of L2, but larger than that of
water.
Calculating Density
• What is the density of a platinum nugget has a
mass of 224.50 g and a volume of 10.0 cm3 ?
• Recall, density is mass/volume.
224.50 g
3
=
22.5
g/cm
10.0 cm3
Specific Heat
• The specific heat of a substance is the amount of
heat required to bring about a change in
temperature.
• It is expressed with units of calories per gram
degree Celsius.
• The larger the specific heat, the more heat is
required to raise the temperature of the substance.
Unit Equations
• A unit equation is a simple statement of two
equivalent quantities.
• For example:
– 1 hour = 60 minutes
– 1 minute = 60 seconds
• Also, we can write:
– 1 minute = 1/60 of an hour
– 1 second = 1/60 of a minute
Unit Conversions
• A unit conversion factor, or unit factor, is a ratio
of two equivalent options.
• For the unit equation 1 hour = 60 minutes, we can
write two unit factors:
1 hour
60 minutes
or
60 minutes
1 hour
Unit Analysis Problem Solving
• An effective method for solving problems in
science is the unit analysis method.
• It is also often called dimensional analysis or the
factor label method.
• There are three steps to solving problems using
the unit analysis method.
Steps in the Unit Analysis Method
1. Write down the unit asked for in the answer
2. Write down the given value related to the answer.
3. Apply a unit factor to convert the unit in the
given value to the unit in the answer.
Unit Analysis Problem
• How many days are in 2.5 years?
• Step 1: We want days.
• Step 2: We write down the given: 2.5 years.
• Step 3: We apply a unit factor (1 year = 365 days)
and round to two significant figures.
365 days
2.5 years 
 910 days
1 year
Another Unit Analysis Problem
• A can of Coca-Cola contains 12 fluid ounces.
What is the volume in quarts (1 qt = 32 fl oz)?
• Step 1: We want quarts.
• Step 2: We write down the given: 12 fl oz.
• Step 3: We apply a unit factor (1 qt = 32 fl oz) and
round to two significant figures.
1 qt
12 fl oz. 
 0.38 qt
32 fl oz.
Another Unit Analysis Problem
• A marathon is 26.2 miles. What is the distance in
yards (1 mi = 1760 yards)?
• Step 1: We want yards.
• Step 2: We write down the given: 26.2 miles.
• Step 3: We apply a unit factor (1 mi = 1760 yards)
and round to three significant figures.
1760 yd
26.2 mi 
 46,100 yd
1mi
Metric Unit Factors
• Since 1000 m = 1 km, we can write the following
unit factors for converting between meters and
kilometers:
1 km
1000 m
or
1000 m
1 km
• Since 1 m = 0.01 cm, we can write the following
unit factors.
1 cm
0.01 m
or
0.01 m
1 cm
Metric-Metric Conversions
• We will use the unit analysis method we learned
in Chapter 2 to do metric-metric conversion
problems.
• Remember, there are three steps
– Write down the unit asked for in the answer
– Write down the given value related to the answer
– Apply unit factor(s) to convert the given unit to the
units desired in the answer.
Metric-Metric Conversion Problem
• What is the mass in grams of a 325 mg aspirin
tablet?
• Step 1: We want grams.
• Step 2: We write down the given: 325 mg.
• Step 3: We apply a unit factor (1 mg = 0.001 g)
and round to three significant figures.
0.001 g
325 mg ×
= 0.325 g
1 mg
Two Metric-Metric Conversions
• A hospital has 125 deciliter bags of blood plasma.
What is the volume in milliliters?
• Step 1: we want the answer in mL
• Step 2: we have 125 dL.
• Step 3: we need to first convert dL to L and then
convert L to mL:
0.1 L
1 dL
and
0.001 mL
1L.
Problem Continued
• Apply both unit factors, and round the answer to 3
significant digits.
• Notice that both dL and L units cancel, leaving us
with units of mL.
0.1 L
1 mL
125 dL ×
×
= 12,500 mL
1 dL
0.001 L
Another Example
• The mass of the Earth is 5.98 × 1024 kg. What is
the mass expressed in megagrams, Mg?
• We want Mg; we have 5.98 × 1024 kg
• Convert kilograms to grams, and then grams to
megagrams.
5.98 ×
1024
1000 g
1 Mg
kg ×
×
= 5.98 × 1021 Mg
1 kg
1000000 g
Metric and English Units
• The English system is still very common in the
United States.
• We often have to convert between English and
Metric Units.
Metric-English Conversion
• Which distance is longer, 100 meters or 100
yards?
• Lets convert 100.0 m to 100 yards given that
1 yd = 0.914 m.
• 100 meters is 109 yards, so 100 yards is shorter.
1 yd
100.0 m ×
= 109 yd
0.914 m
English-Metric Conversion
• A half gallon carton contains 64.0 fl oz of milk.
How many milliliters of milk are in a carton?
• We want mL, we have 64.0 fl oz.
• Use 1 qt = 32 fl oz, and 1 qt = 946 mL.
1 qt
946 mL
64.0 fl oz ×
×
= 1,890 mL
32 fl oz
1 qt
English-Metric Conversion
• A Volkswagen Beetle engine displaces a volume
of 498 cm3 in each cylinder. What is the
displacement in cubic inches, in3?
• We want in3, we have 498 cm3.
• Use 1 in = 2.54 cm three times.
498
cm3
1 in
1 in
1 in
×
×
×
= 30.4 in3
2.54 cm 2.54 cm 2.54 cm
Compound Unit Problem
• A Corvette is traveling at 95 km/hour. What is the
speed in meters per second?
• We have km/h, we want m/s.
• Use 1 km = 1000 m and 1 h = 3600 s.
95 km
1 hr
1000 m
×
×
= 26 m/s
1 km
hr
3600 s
Density as a Unit Factor
• We can use density as a unit factor for
conversions between mass and volume.
• An automobile battery contains 1275 mL of acid.
If the density of battery acid is 1.84 g/mL, how
many grams of acid are in an automobile battery?
• We have 1275 mL and we want grams:
1.84 g
1275 mL ×
= 2350 g
mL
Conclusions
• The basic units in the metric system are grams for
mass, liters for volume, and meters for distance.
• The base units are modified using prefixes to
reduce or enlarge the base units by factors of 10.
• We can use unit factors to convert between metric
units.
• We can convert between metric and English units
using unit factors.
Summary Continued
• A unit equation is a statement of two equivalent
quantities.
• A unit factor is a ratio of two equivalent
quantities.
• Unit factors can be used to convert measurements
between different units.
Conclusions Continued
• Volume is defined as length × width × thickness.
• Volume can also be determined by displacement
of water.
• Density is mass divided by volume.
Conclusions Continued
• Temperature is a measure of the average energy of
the particles in a sample.
• Heat is a measure of the total energy of a
substance.
• Specific heat is a measure of how much heat is
required to raise the temperature of a substance.