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Fractions, Decimals, Percents

Fractions, Decimals, Percents. October, 2011. Reminder…. Numerator represents the… “part” Denominator represents the… “whole” So, Example: There were 15 elephants in the zoo that has 236 animals. Write a fraction representing this situation. Terminating Decimals.

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Fractions, Decimals, Percents

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  1. Fractions, Decimals, Percents October, 2011

  2. Reminder… • Numerator represents the… “part” • Denominator represents the… “whole” • So, • Example: There were 15 elephants in the zoo that has 236 animals. Write a fraction representing this situation.

  3. Terminating Decimals • Examine the decimal below. What do you notice? • 6.375 • Definition: Any decimal that “terminates” • “Terminates” means “to end or stop” • Examples of Terminating Decimals: • 5.67 4.23 • -6.901 -3.75 • A terminating decimal is part of the real number system. How is it classified?

  4. Repeating Decimals • Examine the decimals below. What do you notice? • 6.33333…. • Definition: Any decimal that has a constant pattern of digits that repeat. • Examples: • 5.3333… “3” is the repeating digit • 6.3030… “30” is the repeating pattern • -1.233233… “233” is the repeating pattern

  5. Repeating Decimals • A repeating decimal is part of the real number system. How is it classified? • The line above the repeating digits is called… • Bar Notation

  6. Fractions, Decimals & Percents • All three have the same value, they are just represented in different ways. • We can calculate with fractions AND decimals, but NOT percents!

  7. FRACTIONS TO DECIMALS

  8. Fractions to Decimals • Method 1 • If the denominator is a power of 10 (10, 100, 1000, etc.), then use the place value to write the decimal. 7/10 .7 53/100 .53

  9. Fractions to Decimals • Method 2 • Any fraction can be written as a decimal – • How? • Divide the numerator by the denominator. • YOU MUST BE ABLE TO SHOW THIS USING LONG DIVISION!! 5/8 = .625 2/5 = .40

  10. FRACTIONS TO PERCENTS

  11. Fractions to Percents • Percent means… • “Per 100” or “Out of 100” • Method 1 • Convert fraction to equivalent fraction with denominator of 100. • 1/4 = 25/100 = 25% • 12/25 = 48/100 = 48%

  12. Fractions to Percents • Method 2 • Make the fraction a decimal and multiply by 100 • (move decimal 2 places to right) • 1/4 = .25 = 25% • 12/25 = .48 = 48%

  13. DECIMALS TO PERCENTS

  14. Decimals to Percents • Multiply by 100 (move decimal 2 places to right) • .25 = 25% • .48 = 48%

  15. DECIMALS TO FRACTIONS

  16. Decimals to Fractions • “SAY” the decimal and create the fraction using the place value as the denominator…then, simplify! • .35 = 35/100 = 7/20 • .217 = 217/1000

  17. Repeating Decimals to Fractions • How do you make a repeating decimal into a fraction? • There is a very complicated process that ultimately says “take the repeating part of the decimal and put it over a denominator that has the same number of 9’s.” • Example – 0.3333… = 3/9 = 1/3

  18. PERCENTS TO FRACTIONS

  19. Percents to Fractions • Percent = “Per 100” or “Out of 100”… • So create the fraction by removing the % sign and placing the number over 100. • 23% = 23/100 • 55% = 55/100 (simplify)

  20. PERCENTS TO DECIMALS

  21. Percents to Decimals • Divide the percent by 100 (move decimal 2 places to the left) • 23% = 23/100 = .23 • 64% = 64/100 = .64

  22. Practice • Write each fraction as a decimal. • 1/8 5/9 7 ½ • Write each decimal as a fraction. • .22 0.1 4.6

  23. Practice • Write each fraction as a percent. • ¼ 6/10 17/20 • Write each percent as a fraction. • 90% 75% 22%

  24. Practice • Write each percent as a decimal. • 27% 70% 6% • Write each decimal as a percent. • .95 .08 5.8

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