Percents

A percent is a ratio in which a number is compared to 100. For example, the expression 60 percent means “60 out of 100.” The symbol % stands for “percent.”

A percent can be written in decimal form by first writing it in ratio form, and then writing the ratio as a decimal. For example, 25% is equal to the ratio 25 100 25 over 100  or 1 4 . 1 fourth , .  As a decimal, 1 4 1 fourth  is equal to 0.25. Note that 25% can also be written directly as a decimal by moving the decimal point two places to the left.

Example 1

Convert each percent to a decimal.

1. 42%

   42 % = 0.42 42 percent equals , 0.42

2. 157%

   157 % = 1.57 157 percent equals , 1.57

3. 12.4%

   12.4 % = 0.124 12.4 , percent equals , 0.124

4. 4%

   4 % = 0.04 4 percent equals , 0.04

To calculate a percent of a number, write the percent as a decimal and multiply.

Example 2

Simplify. Where necessary, round to the nearest tenth.

1. 30% of 242

   30 %  of  242 = 0.3 ⋅ 242   = 72.6 table with 2 rows and 3 columns , row1 column 1 , 30 percent , of , 242 , column 2 equals , column 3 0.3 dot 242 , row2 column 1 , , column 2 equals , column 3 72.6 , end table

2. 7% of 38

   7 %  of  38 = 0.07 ⋅ 38   = 2.66 ≈ 2.7 table with 2 rows and 3 columns , row1 column 1 , 7 percent , of , 38 , column 2 equals , column 3 0.07 , dot 38 , row2 column 1 , , column 2 equals , column 3 2.66 , almost equal to 2.7 , end table

For a percent problem, it is a good idea to check that your answer is reasonable by estimating it.

Example 3

Estimate 23% of 96.

23 % ≈ 25 % 23 percent almost equal to 25 percent  and 96 ≈ 100 . 96 almost equal to 100 .  So 25 %   ( or 1 4 ) 25 percent open or , 1 fourth , close  of 100 = 25 . 100 equals 25 .

A reasonable estimate is 25.

Exercises

Convert each percent to a decimal.

1. 50%
2. 27%
3. 6%
4. 84.6%
5. 109%
6. 2.5%

Simplify. Where necessary, round to the nearest tenth.

7. 21% of 40
8. 45% of 200
9. 6% of 120
10. 23.8% of 176

Estimate.

11. 12% of 70
12. 48% of 87
13. 73% of 64
14. 77% of 42

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