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

2. 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 = mm
1 lb = oz
2.205 lb = 1 kg

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

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 © by Pearson Education, Inc.
Publishing as Benjamin Cummings

6. 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 cm
2.54 cm 1 in.

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

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

9. 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
$ lb red peppers
Example 2:
The cost of one gallon (1 gal) of gas is $2.34.
1 gallon of gas and $2.34
$ gallon of gas

10. Percent as a Conversion Factor
A percent factor
gives the ratio of the parts to the whole.
% = Parts x 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

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

12. 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

13. 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 g gold
C. One gallon of gas is $2.27
1 gal and $2.27
$ gal