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Chapter 2 Measurements

2.6Writing Conversion Factors

Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings

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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

2.205 lb = 1 kg

Equalities

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Exact and Measured Numbers in Equalities

Equalities between units of

• The same system are definitions and use exact numbers.

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

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Some Common Equalities

Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

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Equalities on Food Labels

The contents of packaged foods

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

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

Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

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A conversion factor • Is a fraction obtained from an equality.

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

denominator.

• Can be 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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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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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 hr = 60 min) 1 hr and 60 min

60 min 1 hr

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

Solution

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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.

Squared (1 in.)2 = (2.54 cm)2

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

(2.54 cm)2 (1 in.)2

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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A conversion factor • May be obtained from information in a word

problem.• Is written for that problem only.

Example:

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

Conversion Factors in a Problem

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

% = Part x 100Whole

• Use matching units to express the percent.• Uses the value 100 and a unit for the whole.• Is 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

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Percent Factor in a Problem

The thickness of the skin foldat the waist indicates 11% bodyfat. What percent factors can bewritten for body fat in kg?

Percent factors using kg

11 kg fat and 100 kg mass

100 kg mass 11 kg fat

Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings

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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 is $2.29

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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 jewelry = 18 g gold

18 g gold and 100 g jewelry

100 g jewelry 18 g gold

C. 1 gal gas = $2.29

1 gal and $2.29

$2.29 1 gal