Math in Our World
Section 9.3
Measures of Weight and
Temperature
Learning Objectives
 Converting weights in the English system.
 Converting weights in the metric system.
 Converting weights between English and metric
units.
 Converting temperatures between the Fahrenheit
and Celsius scales.
Units of Weight
English Units
16 ounces (oz) = 1 pound (lb)
2,000 lb = 1 ton (T)
Metric Units
1 kilogram (kg) = 1,000 grams (g)
1,000 kg = 1 metric ton (t)
English/Metric Conversions
1 kg ≈ 2.2 lb
1 oz ≈ 28 g
EXAMPLE 1
Converting Weights in the
English System
According to the Guinness Book of World
Records, the largest healthy baby ever delivered
weighed 360 ounces. How much did he weigh in
pounds?
SOLUTION
360oz
1lb

16oz
1
 22.5lb
This is almost exactly 3 times as large as an average
newborn boy!
EXAMPLE 2
Converting Weights in the
English System
An empty Boeing 747 weighs about 175 tons. How
much does it weigh in ounces?
SOLUTION
We will need to first convert tons to pounds, then pounds to
ounces.
175T 2, 000lb 16oz
 5,600,000oz


1T
1lb
1
EXAMPLE 3
Converting Metric Units of
Weight
Convert each of the following:
(a) 150 grams of protein powder to milligrams
(b) 23 grams of salt to kilograms
(c) 3 kilograms of chicken to milligrams
EXAMPLE 3
Converting Metric Units of
Weight
(a) 150 grams of protein powder to milligrams
SOLUTION
For reference, here is the order of the metric prefixes from
largest to smallest: kilo, hecto, deka, base unit, deci, centi, milli.
The prefix milli is three steps below the base unit, so multiply
by 1,000 (or move the decimal three places right).
150 g 10
3
 150 0 0 0  150,000mg
EXAMPLE 3
Converting Metric Units of
Weight
(b) 23 grams of salt to kilograms
SOLUTION
For reference, here is the order of the metric prefixes from
largest to smallest: kilo, hecto, deka, base unit, deci, centi, milli.
The prefix kilo is three units above the base unit, so divide by
1,000 (or move the decimal three places left).
23 g 10
 0 23  0.023kg
3
EXAMPLE 3
Converting Metric Units of
Weight
(c) 3 kilograms of chicken to milligrams
SOLUTION
For reference, here is the order of the metric prefixes from
largest to smallest: kilo, hecto, deka, base unit, deci, centi, milli.
The prefix milli is six steps below the prefix kilo, so multiply
by 1,000,000 (which is easy in this case, without moving the
decimal).
3 kg x 1,000,000 = 3,000,000 mg
EXAMPLE 4
Converting Between English
and Metric Units of Weight
(a) The heaviest amount ever successfully lifted in
Olympic competition was in the clean and jerk
competition in Athens in 2004: 263.5 kg. How
many pounds is that?
(b) An average adult hummingbird weighs oneeighth of an ounce. How many grams does it
weigh?
EXAMPLE 4
Converting Between English
and Metric Units of Weight
SOLUTION
(a) Using dimensional analysis:
263.5kg 2.2lb
 579.7lb

1
1kg
(b) Using dimensional analysis:
1
28 g 28
oz 
 g  3.5 g
8
8
1oz
EXAMPLE 5
Assessing Weight Loss
Megan decides that she absolutely will not go to
Florida for spring break unless she loses 15
pounds in the next 3 months. She finds an
advertisement online for a British weight loss
system that guarantees loss of 3 kg per month. If
that claim is true, will she reach her goal?
EXAMPLE 5
Assessing Weight Loss
SOLUTION
We can do this in one calculation by multiplying by the unit
fraction 2.2 lb/1 kg to eliminate kg, then multiplying by 3
months:
3kg
2.2lb

 3 months  19.8lb
1 month 1kg
If the claim is accurate (a very big if), Megan should start
saving money for her trip.
Conversions for Temperature
Temperature is measured in the English system
using degrees Fahrenheit. On this scale, water
freezes at 32° and boils at 212°. The average
temperature of the human body is 98.6°.
In the metric system, temperatures are measured
in degrees Celsius (also known as centigrade).
Like all metric measurements, the Celsius scale is
based on powers of 10 in some form: water
freezes at 0° and boils at 100°. The average
temperature of the human body is 37°.
Conversions for Temperature
Fahrenheit-Celsius Conversions
To convert Celsius to Fahrenheit:
9
F  C  32
5
To convert Fahrenheit to Celsius:
5
C   F  32 
9
EXAMPLE 6
Converting Celsius to
Fahrenheit
In preparing for vacation, Randy and Catalina
check the Internet and find that the average
temperature over the next week at their destination
is predicted to be 28° Celsius. Should they pack
coats or bathing suits?
SOLUTION
Substitute 28 for C in the first formula:
Swimsuits and
sunblock it is!
EXAMPLE 7
Converting Fahrenheit to
Celsius
A frozen pizza needs a 450° Fahrenheit oven to
cook. Suppose you bought a cheap oven on eBay,
and found that it had been scavenged from
Romania, so the temperatures on the dial are
Celsius. At what temperature should you set the
oven?
SOLUTION
Substitute F = 450
into the second
formula:
You should set it close to 230°.