5.2 Percent Converting Between Fractions, Decimals, And Percents Worksheet
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105.2 Percent: Converting Between Fractions, Decimals, and Percents
The concept of percent permeates most common uses of mathematics in everyday life. We pay
taxes based on percents, many people earn income as a percent sales commission, investments
and banks compare alternatives using percent, and sports team records are represented as a
percent. A percent is a ratio compared with 100. When we pay 7.25% sales tax, we pay $7.25
tax for every $100 in sales price. As a ratio, this can be written as:
$7.25 tax
= 0.0725
$100 price
Since the denominator of a percent is 100, we can easily convert percents to decimals by
dividing by 100. Recall this involves moving the decimal point two place values to the left.
Similarly, we can convert percents to reduced fractions. Given the percent 25%, we convert to
fraction:
25
25 • 1
1
25% =
=
=
100
25 • 4
4
Example 1
Convert each percent to the indicated quantity.
a.
28% to a fraction
b.
19.8% to a decimal
c.
3.5% to a fraction
d.
325% to a decimal
Solution
a.
Writing the percent as a fraction and simplifying:
28
4 • 7
7
28% =
=
=
100
4 • 25
25
b.
Writing the percent as a ratio and dividing:
19.8
19.8% =
= 0.198
100
c.
Writing the percent as a fraction, eliminating decimals, and simplifying:
3.5
10
35
5 • 7
7
3.5% =
=
=
=
•
100
10
1000
5 • 200
200
372
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