Section 9.3Measures of Weight and

Temperature

Math in Our World

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 WeightEnglish Units

16 ounces (oz) = 1 pound (lb) 2,000 lb = 1 ton (T)

Metric Units1 kilogram (kg) = 1,000 grams (g)

1,000 kg = 1 metric ton (t)

English/Metric Conversions1 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

This is almost exactly 3 times as large as an average newborn boy!

360

1

oz 1

16lb

oz22.5 lb

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.

175

1

T 2,000

1

lb

T5,600,000 oz16

1oz

lb

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

150,000 mg

EXAMPLE 3 Converting Metric Units of Weight

(a) 150 grams of protein powder to milligrams

SOLUTION

0.023 kg

EXAMPLE 3 Converting Metric Units of Weight

(b) 23 grams of salt to kilograms

SOLUTION

EXAMPLE 4 Converting Between English and Metric Units of Weight

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?

EXAMPLE 4 Converting Between English and Metric Units of Weight

SOLUTION Using dimensional analysis:

263.5

1

kg 2.2

1

lb

kg579.7 lb

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?

kg

lb

1

2.2

EXAMPLE 5 Assessing Weight Loss

SOLUTION

3

1 month

kg19.8 lbmonths 3

Conversions for TemperatureFahrenheit-Celsius ConversionsTo convert Celsius to Fahrenheit:

To convert Fahrenheit to Celsius:

932

5F C

532

9C F

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?SOLUTIONSubstitute 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?

SOLUTIONSubstitute F = 450 into the second formula:

You should set it close to 230°.

Classwork

p. 503-504: 3-27 odd, 33-39 odd, 53-59 odd, 63-71 odd, 73, 77, 79