1

Chapter 1 Measurements

1.6Writing Conversion Factors

Copyright © 2009 by Pearson Education, Inc.

2

Equalities • use two different units to describe the same measured

amount. • are written for relationships between units of the metric

system, U.S. units, or between metric and U.S. units.

For example,

1 m = 1000 mm

1 lb = 16 oz

2.20 lb = 1 kg

Equalities

3

Exact and Measured Numbers in Equalities

Equalities between units in

• the same system of measurement are definitions that use exact numbers.

• different systems of measurement (metric and U.S.) use measured numbers that have significant figures.

Exception:

The equality 1 in. = 2.54 cm has been defined as an exact relationship. Thus, 2.54 is an exact number.

4

Some Common Equalities

39.4 in.

1.06 qt

946 mL = 1 qt

5

Equalities on Food Labels

The contents of packaged foods • in the U.S. are listed in both metric and U.S.

units.

• indicate the same amount of a substance in two different units.

Copyright © 2009 by Pearson Education, Inc.

6

A conversion factor is• obtained from an equality.

Equality: 1 in. = 2.54 cm

• written as a fraction (ratio) with a numerator and denominator.

• inverted to give two conversion factors for every equality. 1 in. and 2.54 cm

2.54 cm 1 in.

Conversion Factors

7

Write conversion factors from the equality for each of the following.

A. liters and mL

B. hours and minutes

C. meters and kilometers

Learning Check

8

Write conversion factors from the equality for each of the following.

A. 1 L = 1000 mL 1 L and 1000 mL 1000 mL 1 L

B. 1 h = 60 min 1 h and 60 min 60 min 1 h

C. 1 km = 1000 m 1 km and 1000 m 1000 m 1 km

Solution

9

A conversion factor • may be obtained from information in a word problem.• is written for that problem only.

Example 1: The price of one pound (1 lb) of red peppers is $2.39.

1 lb red peppers and $2.39$2.39 1 lb red peppers

Example 2: The cost of one gallon (1 gal) of gas is $2.89.

1 gallon of gas and $2.89$2.89 1 gallon of gas

Conversion Factors in a Problem

10

A percent factor• gives the ratio of the parts to the whole.

% = parts x 100whole

• uses the same unit in the numerator and denominator.• uses the value 100.• can be written as two factors.

Example: A food contains 30% (by mass) fat.

30 g fat and 100 g food100 g food 30 g fat

Percent as a Conversion Factor

11

Percent Factor in a Problem

The thickness of the skin fold atthe waist indicates 11% bodyfat. What factors can bewritten for percent body fat (inkg)?

Percent factors using kg:

11 kg fat and 100 kg mass

100 kg mass 11 kg fat

Copyright © 2009 by Pearson Education, Inc.

12

Smaller Percents: ppm and ppb

Small percents are shown as ppm and ppb.

• Parts per million (ppm) = mg part/kg wholeExample: The EPA allows 15 ppm cadmium in food colors

15 mg cadmium = 1 kg food color

• Parts per billion ppb = g part/kg wholeExample: The EPA allows10 ppb arsenic in public water

10 g arsenic = 1 kg water

13

Arsenic in Water

Write the conversion factors for 10 ppb arsenic in public water from the equality

10 g arsenic = 1 kg water.

Conversion factors:

10 g arsenic and 1 kg water 1 kg water 10 g arsenic

Study Tip: Conversion Factors

An equality

• is written as a fraction (ratio).• provides two conversion factors that are the

inverse of each other.

14

15

Learning Check

Write the equality and conversion factors for each of thefollowing.

A. meters and centimeters

B. jewelry that contains 18% gold

C. One gallon of gas is $2.89

16

Solution

A. 1 m = 100 cm 1m and 100 cm

100 cm 1m

B. 100 g jewelry = 18 g gold 18 g gold and 100 g jewelry

100 g jewelry 18 g gold

C. 1 gal gas = $2.89

1 gal and $2.89 $2.89 1 gal

Risk-Benefit Assessment

A measurement of toxicity is

• LD50 or “lethal dose.”

• the concentration of the substance that causes death

in 50% of the test animals.

• in milligrams per kilogram (mg/kg or ppm) of body mass.

• in micrograms per kilogram ( g/kg or ppb) of body

mass.

17

Learning Check

The LD50 for aspirin is 1100 ppm. How many grams of

aspirin would be lethal in 50% of persons with a body mass of 85 kg?

A. 9.4 g

B. 94 g

C. 94 000 g

18

Copyright © 2009 by Pearson Education, Inc.

Solution

The LD50 for aspirin is 1100 ppm. How many grams of

aspirin would be lethal in 50% of persons with a body mass of 85 kg?

B. 94 g

1100 ppm = 1100 mg/kg body mass

19

85 kg1100 mg

kg

1 g

1000 mg = 94 g