Section 4.2
Using Tables for Conversions
Pre-Activity
Preparation
Immigrants to the United States face many challenges. One is certainly
our quirky resistance to convert to the metric system of measurement. The
following scenario illustrates the point.
At a social gathering of a neighborhood watch group, two moms were trading
recipes. Maria, a recent emigrant from Chile, wanted Sherri’s recipe for
Mississippi Mud Cake. Sherri supplied the recipe at right from her mother’s
favorite recipe file:
Unfortunately, Maria’s experience with baking was
limited to using only metric weights and measures.
Undaunted, she accepted the recipe and vowed to
make the necessary conversions so that she could
make a delicious family treat.
Mississippi Mud Cake
2 cups all-purpose flour
2 cups sugar
1 teaspoon baking soda
1/2 teaspoon salt
1/2 pound butter
1/3 cup cocoa
1 cup water
1/2 cup buttermilk
2 eggs, lightly beaten
1 teaspoon vanilla
8 ounces mini marshmallows
2 cups chocolate icing
A little history on international measurement from www.bipm.org:
The Convention of the Metre (Convention du Mètre) is a treaty which gives authority to the General
Conference on Weights and Measures (CGPM), the International Committee for Weights and Measures
(CIPM) and the International Bureau of Weights and Measures (BIPM) to act in matters of world metrology,
particularly concerning the demand for measurement standards of ever increasing accuracy, range and
diversity, and the need to demonstrate equivalence between national measurement standards.
The Convention was signed in Paris in 1875 by representatives of seventeen nations. As well as founding
the BIPM and laying down the way in which the activities of the BIPM should be financed and managed,
the Metre Convention established a permanent organizational structure for member governments to act
in common accord on all matters relating to units of measurement.
The Convention, modified slightly in 1921, remains the basis of international agreement on units of
measurement. There are now fifty-one Member States, including all the major industrialized countries.
Learning Objectives
• Understand that a measurement may be expressed in different units
• Apply the Methodology for Solving a Proportion to calculate conversions between units
• Use unit analysis for validation
Terminology
Previously Used
New Terms
to
Learn
metric
unit
unit analysis
285
Chapter 4 — Tables and Simple Statistics
286
Building Mathematical Language
English Units
In the United States, we use measurements of inches, feet, yards, and miles to show distances. To measure
weight we use ounces, pounds and tons; and to measure volume we use ounces, cups, pints, quarts and
gallons. These units are part of the English Measurement System and have been used for hundreds of
years.
The following chart lists some common English measurement conversions.
Length
Weight
Volume/Capacity
12 inches (in) = 1 foot (ft)
16 ounces (oz) = 1 pound (lb)
8 fluid ounces = 1 cup (c)
3 feet = 1 yard (yd)
2000 pounds = 1 ton (T)
2 cups = 1 pint (pt)
5280 feet = 1 mile (mi)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
Metric Units
The metric system of measurement was developed as a system that was simple to convert between units
of the same measure and between units of volume, weight, and length. The metric system is the scientific
standard of measurement used throughout the world. The following chart illustrates the connection between
the metric system and place value.
Place Name
Place Value
Metric Name/Prefix
thousandth
0.001
milli–
hundredth
0.01
centi–
tenth
0.1
deci–
one
1
meter, gram, liter
ten
10
deka–
hundred
100
hecto–
thousand
1000
kilo–
Use the following equivalents to convert between metric units.
Length
Weight
Volume
1 meter (m) = 1000 millimeters (mm)
1 gram (g) = 1000 milligrams (mg) 1 liter (L) = 1000 milliliters (mL)
1 meter = 100 centimeters (cm)
1 kilogram (kg) = 1000 grams
1 kilometer (km) = 1000 meters (m)
1 metric ton (t) = 1000 kilograms
1 liter = 10 deciliters
1 centimeter = 10 millimeters
Length and volume are fundamentally related in the metric system:
1 cubic centimeter (cm3) = 1 milliliter
Section 4.2 — Using Tables for Conversions
287
Converting between Systems
Sometimes it is necessary to change from English to metric units or metric to English units. The following
table lists some commonly used conversions between metric and English units.
Metric to English
Length
Weight
Volume
English to Metric
1 centimeter ≈ 0.3937 inches
1 inch = 2.54 centimeters
1 meter ≈ 3.28 feet
1 foot = 0.3048 meters
1 kilometer ≈ 0.62 miles
1 mile ≈ 1.6 kilometers
1 kilogram ≈ 2.2 pounds
1 pound ≈ 0.45 kilograms
1 gram ≈ 0.035 ounces
1 ounce ≈ 28.3 grams
1 liter ≈ 4.23 cups
1 cup ≈ 236.6 milliliters
1 liter ≈ 1.057 quarts
1 quart ≈ 0.946 liters
Note: Use the internet to find other conversion tables and even conversion calculators. Sites like www.
infoplease.com and www.factmonster.com have tables set up so that you can easily calculate between
units as well as explore many more measurements than presented here. Enter “unit conversions” in the
search space provided by your internet search engine and see thousands of hits on the topic.
Applying Proportions
Complications arise when we need to calculate measurements that have different units. It is necessary to
convert between units for the same reason we find common denominators when working with fractions:
we need to compare or calculate with “like” sizes.
Many conversions can be done mentally, and almost automatically. We can quickly convert 15 yards to
45 feet, or 1.5 pounds to 24 ounces, or six cups to three pints. We quickly multiply or divide by a known
equivalent: 1 yard = 3 feet; 1 pound = 16 ounces; 1 cup = ½ pint, to name a few.
Sometimes comparing or changing units is not easy enough that we can convert units mentally. When that
is the case, we can use proportions to change from one unit to another. The methodology on the following
page can be used for converting between any two measurements.
Unit Analysis (also known as “Dimensional Analysis”)
1 yd
= 2 yd
one unit to another. For example, let’s convert 6 feet into yards:
3 ft
We can perform unit analysis to determine that we have started and finished with the correct units:
Unit analysis is a way to validate the correct conversion from
6 ft :
ft : yd
= yd , validating that our answer should be in yards.
ft
While this is a relatively simple example, the more complicated the conversion problem, the more useful
unit analysis becomes. While none of the problems in this section will be this complex, the conversion
from 55 miles per hour to meters per second is shown below. You can see how unit analysis allows us to
make sure that our calculation follows accurate conversions from beginning to end:
55 mile 5280 feet 1 meter
1 hour
1 minute
55 : 5280
meters
:
:
:
:
=
. 24.59
second
1 hour
1 mile
3.28 feet 60 minute 60 seconds 3.28 : 60 : 60
Chapter 4 — Tables and Simple Statistics
288
Methodologies
Calculating a Conversion
► Example 1: A recipe instructs you to use a half a cup of butter in the recipe but the wrapper only shows
the butter divided into ounces. How many ounces do you need?
►
Example 2: A recipe for beer cheese calls for ¾ cup
of beer. How many ounces is that?
Steps in the Methodology
Step 1
Locate the
conversion in a table
Step 2
Incorporate the
table values and the
units for conversion
into a model (set up
a proportion)
Step 3
Test that units
align and perform
a unit analysis
to determine the
correct units for the
answer
Obtain the appropriate
conversion table and
the conversion needed.
Set up a proportion
using the information
from the table and the
measurement you need
to convert.
Represent the unknown
measurement with a
variable.
Make sure the units
match in the proportion.
Try It!
Example 1
Look under volume for
the conversion:
1 cup = 8 ounces
Set up using a proportion:
1
c
2 = 1c
x
8 oz
cup
cup
=
ounces ounces
Changing cups (c) to
ounces (oz); cups divide
out, leaving ounces as
the unit for the answer:
c : oz = c : x
c : oz
=x
c
Step 4
Calculate the
conversion
Solve the proportion for
the conversion.
Cross multiply and solve:
1
c : 8oz = 1c : x
2
1
c : 8oz
2
=x
1c
1
: 8oz = x
2
Answer: x = 4oz
Example 2
Section 4.2 — Using Tables for Conversions
289
Steps in the Methodology
Step 5
Validate your
calculation by
converting back to
the original unit and
comparing answers
Example 1
For comparison
problems worked in
one unit, rework the
problem in the other
unit and compare
answers.
Example 2
8 oz = 1 c
4 oz 8 oz
=
x
1c
oz oz
=
c
c
4 oz : 1 c
x=
8 oz
1
x= c
2
1
1
c= c 
2
2
Models
Model 1A: English Measures (length)
Which is longer: 17 inches or 1.3 feet?
Step 1
Conversion factor
Step 2
Proportion
Step 3
Unit Analysis
Step 4
Calculate
Step 5
Working in feet:
Answer:
Working in inches:
Convert to feet (ft)
12 in = 1 ft
Convert to inches (in)
1 ft = 12 in
17 in 12 in
=
x
1 ft
1.3 ft 1 ft
=
x
12 in
in in
=

ft ft
in : ft
= ft
in
17 in : 1 ft = x : 12 in
Validate
or
ft ft

=
in in
ft : in
= in
ft
1.3 ft : 12 in = x : 1 ft
17 in : 1 ft
=x
12 in
1.4 ft . x
17 inches ≈ 1.4 feet
1.3 ft : 12 in
=x
1 ft
15.6 in = x
1.3 feet = 15.6 inches
1.4 ft 1 ft
=
x
12 in
1.4 ft : 12 in
x=
1 ft
x . 16.8 in . 17 in 
15.6 in 12 in
=
x
1 ft
15.6 in : 1 ft
x=
12 in
x . 1.3 ft = 1.3 ft 
17 inches ≈ 1.4 feet, longer
than 1.3 feet, so 17 inches is
longer than 1.3 feet.
1.3 feet = 15.6 inches, shorter
than 17 inches, so 17 inches is
longer than 1.3 feet.
Chapter 4 — Tables and Simple Statistics
290
Model 1B: English Measures (weight)
Which is heavier: 14.3 ounces or 0.81 pounds?
Step 1
Working in pounds:
Conversion factor
or
Working in ounces:
Convert to pounds (lb)
16 oz = 1 lb
Convert to ounces (oz)
1 lb = 16 oz
14.3 oz 16 oz
=
x
1 lb
0.81 lb 1 lb
=
x
16 oz
Step 2
Proportion
Step 3
Unit analysis
oz oz ,
=
lb lb
Step 4
Calculate
16 oz : x = 14.3 oz : 1 lb
0.81 lb : 16 oz = x : 1 lb
x=
x=
lb lb ,
=
oz oz
oz : lb
= lb
oz
14.3 oz : 1 lb
16 oz
x . 0.9 lb
Step 5
Validate
Answer:
lb : oz
= oz
lb
0.81 lb : 16 oz
1 lb
x . 13 oz
14.3 ounces ≈ 0.9 pounds
0.81 pounds ≈ 13 ounces
0.9 lb 1 lb
=
x
16 oz
0.9 lb : 16 oz
x=
1 lb
x . 14.4 oz . 14.3 oz 
13 oz 16 oz
=
x
1 lb
13 oz : 1 lb
x=
16 oz
x . 0.81 oz = 0.81 oz 
14.3 ounces ≈ 0.9 pounds,
heavier than 0.81 pounds, so
14.3 ounces is heavier than
0.81 pounds.
0.81 pounds ≈ 13 ounces,
lighter than 14.3 ounces, so
14.3 ounces is heavier than
0.81 pounds.
Model 1C: English Measures (volume)
Which is more: 2.5 cups or 1.3 pints?
Step 1
Conversion factor
Step 2
Proportion
Step 3
Unit analysis
Working in cups:
Convert to cups (c)
1 pt = 2 c
1.3 pt 1 pt
=
x
2c
pt pt ,
=
c
c
pt : c
pt
=c
or
Working in pints:
Convert to pints (pt)
2 c = 1 pt
2.5 c 2 c
=
x
1 pt
c
c
= ,
pt pt
c : pt
= pt
c
Section 4.2 — Using Tables for Conversions
Step 4
291
2.5 c : 1 pt = x : 2 c
1.3 pt : 2 c = x : 1 pt
Calculate
1.3 pt : 2 c
1 pt
2.5 c : 1 pt
=x
2c
1.25 pt = x
=x
2.6 c = x
2.5 cups = 1.25 pints
1.3 pints = 2.6 cups
Step 5
1.25 pt 1 pt
=
x
2c
1.25 pt : 2 c
x=
1 pt
2.6 c 2 c
=
x
1 pt
Validate
2.6 c : 1 pt
2c
x = 1.3 pt = 1.3 pt 
x=
x = 2.5 c = 2.5 c 
Answer: 1.3 pints = 2.6 cups, more than
2.5 cups, so 1.3 pints is more
than 2.5 cups.
2.5 cups = 1.25 pints, less than
1.3 pints, so 1.3 pints is more
than 2.5 cups.
Model 2A: Metric Measures (length)
Which is longer: 58 centimeters or 0.59 meters?
Step 1
Conversion factor
Step 2
Proportion
Step 3
Unit analysis
Step 4
Calculate
Working in meters:
Convert to centimeters (cm)
1 m = 100 cm
58 cm 100 cm
=
x
1m
0.59 m
1m
=
x
100 cm
cm cm ,
=
m
m
cm : m
=m
cm
58 cm : 1 m = 100 cm : x
58 centimeters = 0.58 meters
Step 5
Validate
Working in centimeters:
Convert to meters (m)
100 cm = 1 m
58 cm : 1 m
=x
100 cm
0.58 m = x
Shortcut:
or
m
m , m : cm
=
= cm
cm cm
m
0.59 m : 100 cm = 1 m : x
0.59 m : 100 cm
=x
1m
59 cm = x
0.59 meters = 59 centimeters
cm to m: move the decimal 2 places to the left (replace cm with m): 58.0 cm = 0.58 m
m to cm: move the decimal 2 places to the right (replace m with cm): 0.59 m = 59.0 cm
0.58 m × 100 = 58 cm
58 cm = 58 cm 
Answer: 58 centimeters = 0.58 meters,
shorter than 0.59 meters, so
0.59 meters is longer than 58
centimeters.
59 cm ÷ 100 = 0.59 m
0.59 m = 0.59 m 
0.59 meters = 59 centimeters,
longer than 58 centimeters, so
0.59 meters is longer than 58
centimeters.
Chapter 4 — Tables and Simple Statistics
292
Model 2B: Metric Measures (weight)
Which is heavier: 975 grams or 1.01 kilograms?
Step 1
Conversion factor
Step 2
Proportion
Step 3
Unit analysis
Step 4
Calculate
Working in grams:
Convert to kilograms (kg)
1000 g = 1 kg
1.01 kg
1 kg
=
x
1000 g
975 g 1000 g
=
x
1 kg
kg kg ,
=
g
g
kg : g
kg
=g
1.01 kg : 1000 g = 1 kg : x
1.01 kg : 1000 g
=x
1010 g = x
1.01 kilograms = 1010 grams
Step 5
Validate
Working in kilograms:
Convert to grams (g)
1 kg = 1000 g
1 kg
Shortcut:
or
g
g
,
=
kg kg
g : kg
g
= kg
975 g : 1 kg = 1000 g : x
975 g : 1 kg
1000 g
=x
0.975 kg = x
975 grams = 0.975 kilograms
kg to g: move the decimal 3 places to the right (replace kg with g): 1.01 kg = 1010 g
g to kg: move the decimal 3 places to the left (replace g with kg): 975 g = 0.975 kg
1010 g ÷ 1000 = 1.01 kg
1.01 kg = 1.01 kg 
Answer: 1.01 kilograms = 1010 grams,
heavier than 975 grams, so
1.01 kilograms is heavier
than 975 grams.
0.975 kg × 1000 = 975 g
975 g = 975 g 
975 grams = 0.975 kilograms,
lighter than 1.01 kilograms,
so 1.01 kilograms is heavier
than 975 grams.
Section 4.2 — Using Tables for Conversions
293
Model 2C: Metric Measures (volume)
Which is more: 253 milliliters or 0.3 liters?
Step 1
Conversion factor
Step 2
Proportion
Step 3
Unit analysis
Step 4
Calculate
Working in milliliters:
Step 5
Working in liters:
Convert to milliliters (mL)
1 L = 1000 mL
Convert to liters (L)
1000 mL = 1 L
0.3 L
1L
=
x
1000 mL
253 mL 1000 mL
=
x
1L
L
L ,
=
mL mL
L : mL
= mL
L
0.3 L : 1000 mL = 1 L : x
0.3 L : 1000 mL
=x
1L
300 mL = x
0.3 liters = 300 milliliters
Shortcut:
or
mL mL ,
=
L
L
mL : L
=L
mL
253 mL : 1 L = 1000 mL : x
253 mL : 1 L
=x
1000 mL
0.253 L = x
253 milliliters = 0.253 liters
L to mL: move the decimal 3 places to the right (replace L with mL): 0.3 L = 300 mL
mL to L: move the decimal 3 places to the left (replace mL with L): 253 mL = 0.253 L
Validate
Answer:
300 mL ÷ 1000 = 0.3 L
0.3 L = 0.3 L 
0.253 L × 1000 = 253 mL
253 mL = 253 mL 
0.3 liters = 300 milliliters,
more than 253 milliliters, so
0.3 liters is more than 253
milliliters.
253 milliliters = 0.253 liters, less
than 0.3 liters, so 0.3 liters is
more than 253 milliliters.
Did you notice?
To change units within the metric system use place value. Multiply
or divide by the power of ten that separates the two measurements.
When converting from a smaller unit to a larger unit, multiply. When
converting from a larger unit to a smaller unit, divide.
Chapter 4 — Tables and Simple Statistics
294
Model 3a: Converting between Metric and English Measures
Feet to Meters: Convert 4.5 feet to meters
Step 1
Conversion factor
Step 2
Proportion
Step 3
Unit analysis
Step 4
Calculate
1 foot ≈ 0.3048 meters
4.5 ft
1 ft
=
x
0.3048 m
ft ft ,
=
m m
ft : m
=m
ft
4.5 ft : 0.3048 m = 1 ft : x
4.5 ft : 0.3048 m
1 ft
x . 1.372 m
x=
Answer: 4.5 feet ≈ 1.372 meters
Step 5
Validate
1.372 m 0.3048 m
=
x
1 ft
1.372 m : 1 ft
x=
0.3048 m
x . 4.501 ft . 4.5 ft 
Model 3b: Converting between Metric and English Measures
Kilometers to Miles: Convert 120 kilometers to miles
Step 1
Conversion factor
1 kilometer ≈ 0.62 miles
Step 2
Proportion
Step 3
Unit analysis
km km ,
=
mi mi
Step 4
Calculate
120 km : 0.62 mi = 1 km : x
120 km
1 km
=
x
0.62 mi
km : mi
= mi
km
120 km : 0.62 mi
1 km
x . 74.4 mi
x=
Answer: 120 kilometers ≈ 74.4 miles
Step 5
Validate
74.4 mi 0.62 mi
=
x
1 km
74.4 mi : 1 km
x=
0.62 mi
x . 120 km = 120 km 
Section 4.2 — Using Tables for Conversions
295
Model 4: Double Conversion
Convert 3 gallons to liters
While we can convert gallons to quarts and quarts to liters, we have no direct conversion for gallons to
liters. We could break this up into two separate conversions, but because we are able to perform a unit
analysis, we can set up a proportional equation that will allow us to perform both of these conversions
in Step 4. We will simply create a longer proportional relationship in Step 2.
Step 1
Conversion factors
1 gallon = 4 quarts
1 quart ≈ 0.946 liters
Step 2
Proportion
3 gal 1 gal 0.946 qt
=
:
x L 4 qt
1L
Step 3
Unit analysis
Step 4
Calculate
gal gal qt
=
:
L qt L
3 gal 1 gal : 0.946 qt 0.946 gal
=
=
x
4L
4 qt : 1 L
x=
3 gal : 4 L
0.946 gal
=
12 L
. 12.68 L
0.946
Answer: 3 gallons ≈ 12.68 liters
Shortcut:
Because we use unit analysis to verify and
validate our starting and ending units, we can
string together multiple conversion proportions:
x = 3 gal :
4 qt
1 gal
:
1L
12 L
=
. 12.68 L
0.946 qt 0.946
We always arrange our proportions so that all units
cancel except the ones we need for our answer.
Step 5
Validate
Convert 12.68 liters to gallons:
x(in gal) = 12.68 L :
=
0.946 qt
1L
12.68 : 0.946
. 2.99 gal 
4
:
1 gal
4 qt
Chapter 4 — Tables and Simple Statistics
296
Model 5: Problem Solving
You have a planter that is 5 feet long and
18 inches wide. You want to put an attractive
border around the planter. The border is only
sold in 30-centimeter sections. How many do
you need to buy? First, draw a diagram.
18 inches
5.25 feet
The first computation is converting 5.25 feet to the equivalent number of inches in order to calculate the
perimeter.
Step 1
Conversion factor
Step 2
Proportion
Step 3
Unit analysis
1 foot = 12 inches
Step 4
Calculate
5.25 ft : 12 in
1 ft
x = 63 in
5.25 ft 1 ft
=
x
12 in
ft ft ,
=
in in
5.25 ft : 12 in = 1 ft : x
x=
ft : in
= in
ft
We now know that 5.25 feet = 63 inches. Next, we
need to find the perimeter of the planter, using the
converted measurement:
Step 5
Validate
5.25 feet = 63 inches
63 in 12 in
=
x
1 ft
x = 5.25 ft 
P = 2l + 2 w
P = 2(63 in ) + 2(18 in )
P = 126 in + 36 in
P = 162 in
Now we need to convert 162 inches to centimeters:
Step 1
Step 2
Step 3
Conversion
factor
1 in ≈ 2.54 cm
Proportion
162 in
1 in
=
x
2.54 cm
Unit analysis
Step 4 Calculate
162 in : 2.54 cm = 1 in : x
162 in : 2.54 cm
1 in
x . 411.48 cm
x=
in
in , in : cm
=
= cm
cm cm
in
Step 5 Validate
162 in ≈ 411.48 cm
411.48 cm 2.54 cm
=
x
1 in
x = 162 in 
We know that the perimeter ≈ 411.48 cm. Because the border is only
sold in sections that are 30 centimeters long, we must divide the
perimeter by 30 to find out how many sections to buy.
411.48 cm
= 13.716
30 cm
Therefore we need to buy 14 pieces of border.
Section 4.2 — Using Tables for Conversions
297
Addressing Common Errors
Issue
Incorrect
Process
Not converting
to a common
unit for
comparison
Which is more: two
2-liter bottles of cola
or a 12 pack of 12 oz
cans?
Two 2-liter colas
because they’re large
bottles, rather than
small cans.
Correct
Process
Resolution
Convert 12 times 12 ounces (144 ounces) to
quarts:
You must use
common units
when making
comparisons.
You cannot
simply trust
appearance or
your intuition.
144 oz 32 oz
=
x
1 qt
x = 4.5 qt
and then
quarts to
liters:
4.5 qt
1 qt
=
x
0.946 L
x ≈ 4.3 L
OR
x(in qt) = 144 oz :
=
1 qt
32 oz
:
0.946 L
1 qt
144 : 0.946
. 4.3 L
32
Compare 4.3 L to two 2-liters or 4 liters. The
12 pack of 12 oz sodas is more.
Validation
We worked the problem in quarts; to validate our answer, we should convert all our
measures into ounces and perform the comparison that way: Two 2 L bottles = 4 L
Convert 4 L to quarts:
4 L 0.946 L
=
x
1 qt
x . 4.23 qt
Then quarts to ounces:
4.23 qt 1 qt
=
x
32 oz
x . 135.36 oz
OR
x(in oz) = 4 L :
=
1 qt
0.946 L
:
32 oz
1 qt
4 : 32
. 135.31 oz
0.946
Compare 135 oz (the cola in the bottles) with 144 oz (the cola in the cans). The cans
contain more cola. 
Did you notice?
Validating the solution in two separate conversions meant that we
had to approximate twice, thus compounding rounding-off errors.
This second method yields a more precise
answer because we only round off once.
Chapter 4 — Tables and Simple Statistics
298
Incorrect
Process
Issue
Using
incorrect
conversion
information
Convert 30 cm to
inches.
30 cm 3 cm
=
x
1 in
30 cm : 1 in = 3 cm : x
30 cm : 1 in
3 cm
x = 10 in
x=
Correct
Process
Resolution
Converting
from metric
units to English
units (or visa
versa) requires
the use of
conversion
factors that
can be difficult
to remember.
Check your
conversion
factors.
Validation
From the chart,
To validate, we will
1 in ≈ 2.54 cm, not 3 cm convert our answer
in inches back to
centimeters and
30 cm 2.54 cm
compare:
=
x
1 in
11.81 in
1 in
=
30 cm : 1 in = 2.54 cm : x
x
2.54 cm
30 cm : 1 in
x . 29.99 cm
x=
2.54 cm
Compare 29.99 cm
x . 11.81 in
with the original
measurement of
30 cm:
29.99 cm ≈ 30 cm 
Issue
Not converting
to a common
unit before
calculating
area
Incorrect
Process
Correct
Process
Resolution
Units must be the same before Convert 1.5 feet to inches.
A picture frame
measures 1.5 ft by 10 multiplying for area.
1.5 ft 1 ft
in. What is the area
=
x
12 in
of the picture?
x : ft = 1.5 ft : 12 in
1.5 ft • 10 in =
x = 18 in
15 sq in
A = lw
A = 18 in • 10 in
A = 180 in2
Validation
The problem did not specify which units were needed for
the answer. We worked in inches for the correct process, so
we can rework the problem in feet and compare our answers
in order to validate the calculation of area. We begin by
converting 10 inches to feet and the calculate the area in
square feet.
10 in 12 in
=
x
1 ft
x . 0.83 ft
A = lw
A = 1.5 ft • 0.83 ft
A ≈ 1.25 ft2
In order to compare this answer with the answer in square inches, we need convert our
answer in square feet to the equivalent answer in square inches:
12 in × 12 in = 1 ft2 = 144 in2
1.25 ft 2
1 ft 2
=
x
144 in 2
x . 179.28 in 2
179.28 in2 ≈ 180 in2

Section 4.2 — Using Tables for Conversions
Issue
Moving the
decimal point
the wrong
direction when
converting
metric
measures
Not validating
by unit
analysis
Incorrect
Process
Convert 120 L
to mL.
299
Correct
Process
Resolution
If you cannot
remember
which direction
to move
the decimal
point, use the
proportion
methodology
for conversions.
1 L = 1000 mL
120 L
1L
=
x
1000 mL
x : L = 120 L : 1000 mL
Convert 1.6 yards Always perform
a unit analysis
to inches.
yd ft
≠
in in
so the proportion was
not set up properly.
120 L = 0.12 mL
1.6 yd 1 ft
=
x
12 in
x = 19.2 in
in Step 2 to
make sure
the units in
the proportion
match up
correctly.
120 L : 1000 mL
L
x =120, 000 mL
x=
1 yd = 36 in
1.6 yd 1 yd
=
x
36 in
yd yd
Step 2
=
in in
x : 1 yd = 1.6 yd : 36 in
x = 57.6 in
Preparation Inventory
Before proceeding, you should be able to use conversion tables to:
Look up appropriate equivalent measures
Build proportions to convert between units
Use unit analysis to validate conversions
Validation
Convert mL back to L
and compare:
1000 mL = 1 L
120, 000 mL 1000 mL
=
x
1L
120, 000 mL : 1 L
x=
1000 mL
x = 120 L
To validate calculations,
convert inches back
to yards and compare
answers:
36 in = 1 yd
57.6 in 36 in
=
x
1 yd
in in
=
yd yd
57.6 in : 1 yd = x : 36 in
x = 1.6 yd
1.6 yd = 1.6 yd 
Section 4.2
Activity
Using Tables for Conversions
Performance Criteria
• Produce translated values within a system of • Produce translated values from a given system to
measurement.
a new system of measurement
– accuracy
– accuracy
– unit Analysis
– unit Analysis
– validation
– validation
– proper presentation of answer
– proper presentation of answer
Critical Thinking Questions
1. What are the two components of a measurement such as 2.6 m?
2. Some rulers have English and metric units on them. When you use such a ruler to record a length, how do
you ensure that someone else knows what your number means?
300
Section 4.2 — Using Tables for Conversions
301
3. When converting from a smaller unit to a larger unit, what happens to the numerical part of the
measurement?
4. When converting from a larger unit to a smaller unit, what happens to the numerical part of the
measurement?
5. How do you locate a conversion table for your needs?
6. How does checking units help you to make sure your conversion was performed correctly?
Chapter 4 — Tables and Simple Statistics
302
7. What are three “short cuts” you can use to convert from one measure to another?
8. Why do multiple measurement systems exist for a given instrument like a ruler or kitchen measuring
cup?
Tips
for
Success
• Converting units by setting up proportions offers two ways to validate your work. You can examine the
units to confirm that the proportions have been set up correctly and the final unit is the one you want (this
is called unit analysis). You can also validate the solution by setting it back into the proportion and test for
equivalency. (See Foundations of Math, Section 4.2.)
• In the examples given to compare two measures, notice that one way to work the proportion uses division
to reach the solution and the other one uses multiplication. Before calculators, division was much harder to
do, so scientists frequently chose the conversion that required multiplication. Conversion tables are often
set up so that all unit changes can be made using multiplication. These tables list conversion factors (a
factor being part of a product). To convert from one unit to another simply multiply the measurement by
the appropriate conversion factor.
Section 4.2 — Using Tables for Conversions
303
Demonstrate Your Understanding
1. Convert the following to the units indicated:
Problem
a)
12 pints to gallons
b)
6 quarts to pints
c)
6 miles to yards
d)
60 inches to feet
Worked Solution
Validation
Chapter 4 — Tables and Simple Statistics
304
Problem
e)
12,400 pounds to
tons
f)
100 yards to feet
2.
Worked Solution
Validation
Convert the following to the units indicated:
Problem
a)
1.23 meters to
centimeters
b)
176 millimeters to
meters
c)
500 milliliters to
liters
Worked Solution
Validation
Section 4.2 — Using Tables for Conversions
Problem
d)
456 grams to
kilograms
e)
34.6 kilograms to
grams
f)
23.5 centimeters to
millimeters
305
Worked Solution
Validation
Worked Solution
Validation
3. Perform the following conversions:
Problem
a)
15 liters to quarts
b)
28 feet to meters
Chapter 4 — Tables and Simple Statistics
306
Problem
c)
185 pounds to
kilograms
d)
26.5 kilometers to
miles
Worked Solution
Validation
4. Perform the following double conversions:
Problem
a)
2 miles to yards
Worked Solution
Validation
Section 4.2 — Using Tables for Conversions
Problem
b)
307
Worked Solution
Validation
550 grams to
pounds
5. If a baby weighs 6 lb 7 oz and her car seat weighs 3.2 kg, how much do they weigh together?
6. A recipe calls for 750 mL of orange juice, 50 mL lemon juice, 1 liter of pineapple juice and 500 mL of rum.
How large should the container be to hold the punch?
Chapter 4 — Tables and Simple Statistics
308
7. Help Maria convert the following recipe ingredients from English to Metric.
English Metric
2 cups to
_____________
all-purpose flour
2 cups to
_____________
sugar
1 teaspoon to
_____________
baking soda
1/2 teaspoon to
_____________
salt
1/2 pound to
_____________
butter
1/3 cup to
_____________
cocoa
1 cup to
_____________
water
1/2 cup to
_____________
buttermilk
2 eggs, lightly beaten
1 teaspoon to
_____________
vanilla
8 ounces to
_____________
mini marshmallows
Section 4.2 — Using Tables for Conversions
Identify
and
Correct
the
309
Errors
In the second column, identify the error(s) in the worked solution or validate its answer. If the worked solution
is incorrect, solve the problem correctly in the third column and validate your answer.
Worked Solution
1)
Allison wanted to know how
many cups of tomato sauce to add
to a 1.2 L jar of sauce to make 2
liters.
2 Ll – 1.2 L = 0.8 L
She needs to convert 0.8 L to
cups.
1 liter ≈ 4.23 cups
0.8 L
1L
=
x
4.23 c
L L
=
c c
c . 3.4c
Allison will use 3 ½ cups of
tomato sauce.
2)
I have a friend who describes
himself as a “2 meter” man. How
tall is he in inches?
2 m 3.28 ft
=
x
12 in
x = 7.3 ft
3)
Micha needed 11.2 g of iron for
his experiment. He measured out
0.0112 mg.
Identify Errors
or Validate
Correct Process
Chapter 4 — Tables and Simple Statistics
310
Worked Solution
4)
Convert 12.5 gallons to liters.
12.5 gal 4 : 0.946 qt
=
x
L
3.784 : x = 12.5
x . 0.33 L
5)
What is the perimeter of a lot that
measures 57.3 m by 0.34 km?
19.5 m2
Identify Errors
or Validate
Correct Process