Copyright © Cengage Learning. All rights reserved. Functions 1 Basic Concepts

Copyright © Cengage Learning. All rights reserved. Unit 1C Review of Operations with Decimal Fractions and Percent

Copyright © Cengage Learning. All rights reserved. Percent 1.13

4 Percent Percent is the comparison of any number of parts to 100 parts. The word percent means “per hundred.” The symbol for percent is %. You wish to put milk in a pitcher so that it is 25% “full” (Figure 1.34a). (a) This pitcher is 25% full.(b) This pitcher is 83% full. (c) This pitcher is 100% full. Figure 1.34 How full is each pitcher?

5 Percent First, imagine a line drawn down the side of the pitcher. Then imagine the line divided into 100 equal parts. Each mark shows 1%: that is, each mark shows one out of 100 parts.

6 Percent Finally, count 25 marks from the bottom. The amount of milk below the line is 25% of what the pitcher will hold. Note that 100% is a full, or one whole, pitcher of milk. One dollar equals 100 cents or 100 pennies. Then, 36% of one dollar equals 36 of 100 parts, or 36 cents or 36 pennies. (See Figure 1.35.) Figure 1.35

7 Percent To save 10% of your salary, you would have to save $10 out of each $100 earned. When the U.S. government spends 15% of its budget on its debt, interest payments are taking $15 out of every $100 the government collects. A salesperson who earns a commission of 8% receives $8 out of each $100 of goods he or she sells.

8 Percent A car’s radiator holds a mixture that is 25% antifreeze. That is, in each hundred parts of mixture, there are 25 parts of pure antifreeze. A state charges a 5% sales tax. That is, for each $100 of goods that you buy, a tax of $5 is added to your bill. The $5, a 5% tax, is then paid to the state. Just remember: percent means “per hundred.”

9 Changing a Percent to a Decimal

10 Changing a Percent to a Decimal Percent means the number of parts per 100 parts. Any percent can be written as a fraction with 100 as the denominator.

11 Example 1 Change each percent to a fraction and then to a decimal. a. b. c. d. 75 hundredths 45 hundredths 16 hundredths 7 hundredths

12 Changing a Percent to a Decimal To change a percent to a decimal, move the decimal point two places to the left (divide by 100). Then remove the percent sign (%). If the percent contains a fraction, write the fraction as a decimal. For problems involving percents, we must use the decimal form of the percent, or its equivalent fractional form.

13 Changing a Decimal to a Percent

14 Changing a Decimal to a Percent Changing a decimal to a percent is the reverse of what we did in Example 1.

15 Example 4 Write 0.75 as a percent = = 75% 75 hundredths hundredeths means percent

16 Changing a Decimal to a Percent To change a decimal to a percent, move the decimal point two places to the right (multiply by 100). Write the percent sign (%) after the number.

17 Changing a Fraction to a Percent

18 Changing a Fraction to a Percent In some problems, we need to change a fraction to a percent. Changing a Fraction to a Percent 1. First, change the fraction to a decimal. 2. Then change this decimal to a percent.

19 Example 6 Change to a percent. 0.6 = 60% So = 0.6 = 60%. First, change to a decimal by dividing the numerator by the denominator. Then change 0.6 to a percent by moving the decimal point two places to the right. Write the percent sign (%) after the number.

20 Changing a Percent to a Fraction

21 Changing a Percent to a Fraction 1. Change the percent to a decimal. 2. Then change the decimal to a fraction in lowest terms.

22 Example 10 Change 25% to a fraction in lowest terms. 25% = = = So 25% = 0.25 =. First, change 25% to a decimal by moving the decimal point two places to the left. Remove the percent sign (%). Then change 0.25 to a fraction. Reduce it to lowest terms.

23 Changing a Percent to a Fraction Changing a Percent That Contains a Mixed Number to a Fraction 1. Change the mixed number to an improper fraction. 2. Then multiply this result by and remove the percent sign (%).

24 Example 12 Change to a fraction. So First, change the mixed number to an improper fraction. Then multiply this result by and remove the percent sign (%).