1

Chapter 2 Measurements

2.6Writing Conversion Factors

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The mass of a packaged product is listed in both U.S. and metric units.

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

• Examples:

1 m = 1000 mm1 lb = 16 oz2.205 lb = 1 kg

Equalities

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3

Exact and Measured Numbers in Equalities

Equalities between units of

• the same system are definitions and are exact numbers

• different systems (metric and U.S.) use measured numbers and count as significant figures

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4

Some Common Equalities

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5

Equalities on Food Labels

The contents of packaged foods

• are listed as both metric and U.S. units

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

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

The mass of a packaged product is listed in both U.S. and metric units.

6

A conversion factor is• a fraction obtained from an equality

Equality: 1 in. = 2.54 cm• written as a ratio with a numerator and

denominator

• is inverted to give two conversion factors for every equality

1 in. and 2.54 cm 2.54 cm 1 in.

Conversion Factors

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7

Write conversion factors for each pair of units:

A. liters and mL

B. hours and minutes

C. meters and kilometers

Learning Check

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8

Write conversion factors for each pair of units:A. liters and mL (1 L = 1000 mL)

1 L and 1000 mL 1000 mL 1 L

B. hours and minutes (1 h = 60 min) 1 h and 60 min

60 min 1 h

C. meters and kilometers (1 km = 1000 m)1 km and 1000 m 1000 m 1 km

Solution

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9

Factors with Powers

A conversion factor can be squared or cubed on both sides of the equality.

Equality 1 in. = 2.54 cm 1 in. and 2.54 cm

2.54 cm 1 in.Equality squared (1 in.)2 = (2.54 cm)2

(1 in.)2 and (2.54 cm)2

(2.54 cm)2 (1 in.)2

Equality cubed (1 in.)3 = (2.54 cm)3

(1 in.)3 and (2.54 cm)3

(2.54 cm)3 (1 in.)3

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An equality and conversion factors • may be obtained from information in a word

problem• are for that problem only

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

Equality: 1 lb peppers = $2.39Conversion factors:

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

Conversion Factors in a Problem

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

Percent(%) = part x 100 whole

• uses matching units to express the percent• uses the value 100 and a unit for the whole• Example: A food contains 30% (by mass) fat.

Equality: 100 g food = 30 g fatConversion factors:

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

Percent as a Conversion Factor

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12

Percent Factor in a Problem

The thickness of the skin foldat the waist indicates 11% bodyfat. What equality and percentconversion factors can bewritten for body fat in kg? Equality (kg): 100 kg of body mass = 11 kg of fat

Percent conversion factors (kg) 11 kg fat and 100 kg mass 100 kg mass 11 kg fat

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

The thickness of the skin fold at the waist is measured in millimeters (mm) to determine the percent of body fat.

ppm and ppb

Relationships of small percent values are• ppm (parts per million or mg/kg)

• ppb (parts per billion or g/kg)

Example:

A soil sample contains 2 ppm of lead.

Equality: 2 mg of lead = 1 kg of soil

Conversion factors: 2 mg lead and 1 kg soil 1 kg soil 2 mg lead

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Learning Check

Write the equality and conversion factors for each

of the following:A. square meters and square centimeters

B. jewelry that contains 18% gold

C. one gallon of gas costing $3.29 D. a water sample with 55 ppb of chromium (Cr)

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Solution

A. 1 m2 = (100 cm)2

(1m)2 and (100 cm)2

(100 cm)2 (1m)2

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

100 g jewelry 18 g goldC. 1 gal of gas = $3.29

1 gal and $3.29 $3.29 1 galD. 1 kg of water = 55 g of chromium

1 kg water and 55 g chromium

55 g chromium 1 kg water

Basic Chemistry Copyright © 2011 Pearson Education, Inc.