Chapter 1 Measurements 1 5 Writing Conversion Factors

Chapter 1 Measurements 1. 5 Writing Conversion Factors Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings 1

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 = 1 lb = 2. 205 lb = 1000 mm 16 oz 1 kg 2

Exact and Measured Numbers in 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. 3

Some Common Equalities 4

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 © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings 5

Conversion Factors 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 1 in. 6

Learning Check Write conversion factors for each pair of units. A. liters and m. L B. hours and minutes C. meters and kilometers 7

Solution Write conversion factors for each pair of units. A. liters and m. L Equality: 1 L = 1000 m. L 1 L and 1000 m. L 1 L B. hours and minutes 1 hr 60 min and Equality: 1 hr = 60 min 1 hr C. meters and kilometers 1000 m 1 km 1000 m and 1000 m 1 km Equality: 1 km = 8

Conversion Factors in a Problem 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 1 lb red peppers Example 2: The cost of one gallon (1 gal) of gas is $2. 34. 1 gallon of gas and $2. 34 1 gallon of gas 9

Percent as a Conversion Factor A percent factor • gives the ratio of the parts to the whole. % = Parts x 100 Whole • uses the same unit to express the percent. • uses the value 100 and a unit for the whole. • can be written as two factors. Example: A food contains 30% (by mass) fat. 30 g fat 100 g food and 100 g food 30 g fat 10

Percent Factor in a Problem The thickness of the skin fold at the waist indicates 11% body fat. What percent factors can be written for body fat in kg? Percent factors using kg: 11 kg fat and 100 kg mass 11 kg fat Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings 11

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. 27 12

Solution A. square meters and square centimeters (1 m)2 and (100 cm)2 (1 m)2 B. jewelry that contains 18% gold 18 g gold and 100 g jewelry 18 g gold C. One gallon of gas is $2. 27 1 gal and $2. 27 1 gal 13