Page 467 - Basic College Mathematics with Early Integers

444 C HAPTE R 6 I PERCENT

Objective Converting Percents, Decimals, and Fractions

Let’s summarize what we have learned so far about percents, decimals, and fractions:

Summary of Converting Percents, Decimals, and Fractions
• To write a percent as a decimal, replace the % symbol with its decimal
equivalent, 0.01; then multiply.
• To write a percent as a fraction, replace the % symbol with its fraction
1
equivalent, ; then multiply.
100
• To write a decimal or fraction as a percent, multiply by 100%.

If we let p represent a number, below we summarize using symbols.

Write a percent Write a percent Write a number
as a decimal: as a fraction: as a percent:
1
#
p% = p10.012 p% = p # p = p 100%
100

PRACTICE 21 Example 21 36.4% of automobile thefts in the continental United States occur
A family decides to spend no in the South. Write this percent as a decimal and as a fraction.
more than 22.5% of its monthly (Source: National Insurance Crime Bureau)
income on rent.Write 22.5% as Solution:
a decimal and as a fraction.
As a decimal: 36.4%=36.4(0.01)=0.364
1
#
1 36.4 36.4 10 364 4 91 91
As a fraction: 36.4% = 36.4 # = = # = = =
#
100 100 100 10 1000 4 250 250
1
91
Thus, 36.4% written as a decimal is 0.364, and written as a fraction is .
250
Work Practice 21

1
PRACTICE 22 Example 22 An advertisement for a stereo system reads “ off.”What percent
4
Provincetown’s budget for off is this?
waste disposal increased by
1 1
1 times over the budget from Solution: Write as a percent.
4 4
last year.What percent increase
1
1
is this? 1 = 100% = 100 % = 100 % = 25%
#
#
4 4 4 1 4
1
Thus,“ off” is the same as “25% off.”
4
Work Practice 22 Copyright 2012 Pearson Education, Inc.
Note: It is helpful to know a few basic percent conversions. Appendix A.4 contains a
Answers handy reference of percent, decimal, and fraction equivalencies.
9 Also. Appendix A.5 shows how to find common percents of a number.
21. 0.225, 22. 125%
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