Section 10.1 Percent

1. Section 10.1 Percent

2. What You Will Learn • Upon completion of this section, you will be able to: • Convert between a percent, a fraction, and a decimal number. • Solve problems involving percent change. • Solve problems involving percent markup and markdown. • Solve other percent problems.

3. Percent • The word percent comes from the Latin per centum, meaning “per hundred.” • A percent is a ratio of some number to 100.

4. To Change a Fraction to a Percent • 1. Divide the numerator by the denominator to obtain a decimal number. • 2. Multiply the decimal number by 100 (which has the effect of moving the decimal point two places to the right). • 3. Add a percent sign.

5. Example 1: Converting Fractions to Percents • Change each of the following fractions to a percent.

6. Example 1: Converting Fractions to Percents • Solution

7. Example 1: Converting Fractions to Percents • Solution

8. Example 1: Converting Fractions to Percents • Solution

9. To Change a Decimal Number to a Percent • 1. Multiply the decimal number by 100. • 2. Add a percent sign.

10. Example 2: Converting Decimal Numbers to Percents • Change each of the following decimal numbers to a percent. • a) 0.14 b) 0.893 c) 0.7625

11. Example 2: Converting Decimal Numbers to Percents • Solution

12. To Change a Percent to a Decimal Number • Remove the percent sign. • Divide the number by 100.

13. Example 3: Converting a Percent to a Decimal Number • a) Change 35% to a decimal number. • b) Change 69.8% to a decimal number.

14. Example 3: Converting a Percent to a Decimal Number • Solution

15. Percent Change • The percent increase or decrease, or percent change, over a period of time is found by the following formula:

16. Percent Change • If the amount in the latest period is greater than the amount in the previous period, the answer will be positive and indicate a percent increase. • If the amount in the latest period is smaller than the amount in the previous period, the answer will be negative and indicate a percent decrease.

17. Example 5: Most Improved Baseball Team • In 2014, the Major League Baseball team with the most improved record for winning games was the Los Angeles Angels. In 2013, the Angels won 78 games. In 2014, the Angels won 98 games. Determine the percent increase in the number of games won by the Angels from 2013 to 2014.

18. Example 5: Most Improved Baseball Team • Solution There was a 25.6% increase in the number of games won 2013 to 2014.

19. Percent Markup • The following formula represents percent markup or markdown on cost. • A positive answer indicates a markup. • A negative answer indicates a markdown. Percent markup (or markdown) on cost

20. Example 7: Determining Percent Markup Holdren Hardware stores pay $48.76 for glass fireplace screens. They regularly sell them for $79.88. At a sale they sell them for $69.99. Determine a) the percent markup on the regular price. b) the percent markup on the sale price.

21. Example 7: Determining Percent Markup Solution a) The percent markup on the regular price was about 63.8%.

22. Example 7: Determining Percent Markup Solution b) The percent markup on the sale price was about 43.5%.

23. Example 9: Down Payment on a Condominium Home Melissa wishes to buy a condominium home for $189,000. To obtain the mortgage loan, she must pay 20% of the selling price as a down payment. Determine the amount of Melissa’s down payment.

24. Example 9: Down Payment on a Condominium Home Solution x = 20% of the selling price = 0.20 (189,000) = $37,800 Melissa’s down payment will be $37,800.