Chapter 6 Lesson 4Fractions, Decimals, &

PercentsPgs. 281-285

What you will learn:Express percents as fractions and vice versaExpress percents as decimals and vice versa

Vocabulary & Key Concept

Percent (281): a ratio that compares a number to 100

Key Concept (282): To write a percent as a decimal, divide by 100 and remove the percent symbol. To write a decimal as a percent, multiply by 100 and add the percent symbol.

To write a percent as a fraction, express the ratio as a fraction with a denominator of 100. Then simplify if possible. Notice that a percent can be greater than 100% or less than 1%.

Example 1 Percents as Fractions Express each percent as a fraction in simplest form.

A. 30% B. 135%

30 = 3 135 = 27 or 1 100 10 100 20C. 0.2% D. 16 % 0.2 10 = 2 = 1 100 10 1000 500 16 100

50 1 = 50 = 1 3 100 300 6

7 20

2323

Multiply by 10 to eliminate 10the decimal in the numerator.

To write a fraction as a percent, write an equivalent fraction with a denominator of 100.

Example 2: Express each fraction as a percent

A. 4 20 = 80 or 80% 5 20 100

A. 14 12.5 = 175 = 175% 8 12.5 100

Remember that percent means per hundred. In the previous examples, you wrote percents as fractions with 100 in the denominator. Similarly, you can write percents as decimals by dividing by 100.

Example 3: Percents as Decimals A. 61% B. 4% 61 = .61 4 = .04 100 100

C. 223% D. 0.9% 223 = 2.23 .9 = 0.009 100 100

Don’t forget, to divide a number by 100 move the decimal point two places to the left. To multiply a number by 100, move the decimal point two places to the right.

Example 4: Decimals as Percents

Express each decimal as a percent. A. 0.35 .35100 = 35%

B. 0.09 .09100 = 9%

C. 0.0042 0.0042100 = .42%

D. 2.27 2.27100 = 227%

Example 5: Fractions as Percents

Express each fraction as a percent. Round to the nearest tenth percent, if necessary.

A. 7 = .28 = 28% 25 Divide the numerator by the denominator, then move

the decimal two places to the right.

B. 15 = 0.006 = .6% 2500C. 10 = 3.333 = 333.3% 3

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Example 6: Compare Numbers

In a survey, one-fifth of parents said that they buy shoes for their children every 4-5 months while 27% of parents said that they buy shoes twice a year. Which of these groups is larger?

Write one-fifth as a percent. Then compare. 1 = .20 or 20% 5Since 27% is greater than 20%, the group that

said they buy shoes twice a year is larger.

Your Turn!Express each percent as a fraction or mixed number in simplest form AND as a decimal.

A. 65%

B. 117%

C. 0.8%

13 0.6520

1 1.17 17100

1 0.008125

Your Turn, Again!Express each decimal or fraction as a percent. Round to the nearest tenth percent, if necessary.

A. 1.3

B. 3 600

C. 12 9

130%

0.005 = 0.5%

1.3333 = 133.3%

One More!

In a survey, 55% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

Compare 55% and three-fifths.Write three-fifths as a percent.3 = 0.60 = 60%5

55% < 60%So it’s the Daily newspaper.