Page 145 - ArithBook5thEd ~ BCC

92% = 0.92
0.2% = 0.002
138% = 1.38
71.02% = 0.7102

To convert a percent to a fraction (or mixed number), first convert the percent to a decimal, as
above, then express the decimal as a fraction (with a visible denominator), and finally, reduce the fraction
to lowest terms, if needed.

Example 176. Convert 10.8% into a fraction in lowest terms.
Solution. We first write 10.8% as a decimal.

10.8% = 0.108.

Then, we write the decimal as a fraction with a visible denominator. In this case, because there are 3
decimal places, the denominator is 1000.
108
0.108 = .
1000
Finally, the GCF of the numerator and denominator is 4, so we cancel 4 from both of these numbers,
obtaining a fraction in lowest terms:
✘ ✘✿ 27
108 ✘ 108 27
= = .
✘
✘✿ 250
1000 ✘ 1000 250

Here are some common percents with their decimal and fractional equivalents (in lowest terms):
1 1 1 1
10% = 0.1 = , 20% = 0.2 = , 25% = 0.25 = , 50% = 0.5 = .
10 5 4 2
To convert a fraction to a decimal, we just perform long division.

Example 177. Convert 1 4 to a decimal.
Solution. Performing the division 1 ÷ 4, we obtain

0. 2 5
4 1. 00
− 8
20
− 20
0

Thus 1 4 =0.25.

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