1 Chapter 2 Measurements 2.6 Writing Conversion Factors Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

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 lb = 1 kg Equalities

3 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.

4 Some Common Equalities Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

5 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

6 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

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

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 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

9 Factors with Powers A conversion factor Can be squared or cubed on both sides of the equality. Equality1 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

10 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 $ lb red peppers and$2.39 $2.391 lb red peppers Conversion Factors in a Problem

11 A percent factor Gives the ratio of the part to the whole. % = Part x 100 Whole 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 and100 g food 100 g food30 g fat Percent as a Conversion Factor

12 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 100 kg mass 11 kg fat Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

13 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

14 Solution A. 1 m 2 = (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 = $ gal and $2.29 $ gal