Chapter 1 Matter, Measurements, & Calculations 1.10 Writing Conversion Factors & Calculating Percentages Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Equalities 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

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.

Some Common Equalities

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

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 2.54 cm 1 in.

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

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

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 $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 $2.34 1 gallon of gas

Percent as a Conversion Factor A percent factor gives the ratio of the parts to the whole. % = Parts x 100 or Actual x 100 Whole Theoretical 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 and 100 g food 100 g food 30 g fat

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

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

Solution A. square meters and square centimeters (1m)2 and (100 cm)2 (100 cm)2 (1m)2 B. jewelry that contains 18% gold 18 g gold and 100 g jewelry 100 g jewelry 18 g gold C. One gallon of gas is $2.27 1 gal and $2.27 $2.27 1 gal