1 Chapter 1 Measurements 1.6 Writing 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 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 m1 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 $ lb red peppers and$2.39 $2.391 lb red peppers Example 2: The cost of one gallon (1 gal) of gas is $ gallon of gasand $2.89 $2.891 gallon of gas Conversion Factors in a Problem

10 A percent factor gives the ratio of the parts to the whole. % = parts x 100 whole 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 and100 g food 100 g food 30 g fat Percent as a Conversion Factor

11 Percent Factor in a Problem The thickness of the skin fold at the waist indicates 11% body fat. What factors can be written for percent body fat (in kg)? Percent factors using kg: 11 kg fat and 100 kg mass 100 kg mass11 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 whole Example: The EPA allows 15 ppm cadmium in food colors 15 mg cadmium = 1 kg food color Parts per billion ppb =  g part/kg whole Example: 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 water10  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 the following. 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 = $ gal and $2.89 $ gal

Risk-Benefit Assessment A measurement of toxicity is LD 50 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 LD 50 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 g 18 Copyright © 2009 by Pearson Education, Inc.

Solution The LD 50 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