Introduction to Terminating and Repeating Decimals

Understanding terminating decimals with a finite number of digits after the decimal point and repeating decimals with an infinite number of digits following a pattern. Learn how to convert fractions to decimals and vice versa using bar notation for repeating decimals.

• Decimals
• Fractions
• Bar Notation
• Terminating
• Repeating

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1. Lesson1 Terminating and Repeating Decimals

2. Lesson 1: Terminating and Repeating Decimals Objective: SWBAT write fractions as decimals and decimals as fractions. Do Now: Worksheet #1 - 7

3. Lesson 1: Terminating and Repeating Decimals Definitions Terminating decimal has a finite number of digits after the decimal point. Repeating decimal has an infinite number of digits after the decimal point and has a pattern. Bar Notation is used to represent repeating decimals.

4. Lesson 1: Terminating and Repeating Decimals 1/1 = 1/2 = 1/3 = 2/3 = 1/4 = 2/4 = 3/4 = 1/5 = 2/5 = 3/5 = 4/5 = 1/6 = 2/6 = 3/6 = 4/6 = 5/6 = 1/7 = 2/7 = 3/7 = 4/7 = 5/7 = 6/7 = 1/8 = 2/8 = 3/8 = 4/8 = 5/8 = 6/8 = 7/8 = 1/9 = 2/9 = 3/9 = 4/9 = 5/9 = 6/9 = 7/9 = 8/9 = 1/10 = 2/10 = 3/10 = 4/10 = 5/10 = 6/10 = 7/10 = 8/10 = 9/10 =

5. Lesson 1: Terminating and Repeating Decimals 1/1 = 1/2 = 1/3 = 2/3 = 1/4 = 2/4 = 3/4 = 1/5 = 2/5 = 3/5 = 4/5 = 1/6 = 2/6 = 3/6 = 4/6 = 5/6 = 1/7 = 2/7 = 3/7 = 4/7 = 5/7 = 6/7 = 1/8 = 2/8 = 3/8 = 4/8 = 5/8 = 6/8 = 7/8 = 1/9 = 2/9 = 3/9 = 4/9 = 5/9 = 6/9 = 7/9 = 8/9 = 1/10 = .1 2/10 = .2 3/10 = .3 4/10 = .4 5/10 = .5 6/10 = .6 7/10 = .7 8/10 = .8 9/10 = .9

6. Lesson 1: Terminating and Repeating Decimals 1/1 = 1/2 = 1/3 = 2/3 = 1/4 = 2/4 = 3/4 = 1/5 = 2/5 = 3/5 = 4/5 = 1/6 = 2/6 = 3/6 = 4/6 = 5/6 = 1/7 = 2/7 = 3/7 = 4/7 = 5/7 = 6/7 = 1/8 = 2/8 = 3/8 = 4/8 = 5/8 = 6/8 = 7/8 = 1/9 = .111 1/10 = .1 2/9 = .222 . 2/10 = .2 3/9 = .333 3/10 = .3 4/9 = .444 4/10 = .4 5/9 = .555 5/10 = .5 6/9 = .666 6/10 = .6 7/9 = .777 7/10 = .7 8/9 = .888 8/10 = .8 9/10 = .9

7. Lesson 1: Terminating and Repeating Decimals 1/1 = 1.0 1/2 = .5 1/3 = .333 2/3 = .666 1/4 = 2/4 = 3/4 = 1/5 = 2/5 = 3/5 = 4/5 = 1/6 = 2/6 = 3/6 = 4/6 = 5/6 = 1/7 = 2/7 = 3/7 = 4/7 = 5/7 = 6/7 = 1/8 = 2/8 = 3/8 = 4/8 = 5/8 = 6/8 = 7/8 = 1/9 = .111 1/10 = .1 2/9 = .222 . 2/10 = .2 3/9 = .333 3/10 = .3 4/9 = .444 4/10 = .4 5/9 = .555 5/10 = .5 6/9 = .666 6/10 = .6 7/9 = .777 7/10 = .7 8/9 = .888 8/10 = .8 9/10 = .9

8. Lesson 1: Terminating and Repeating Decimals 1/1 = 1.0 1/2 = .5 1/3 = .333 2/3 = .666 1/4 = .25 2/4 = .5 3/4 = .75 1/5 = .2 2/5 = .4 3/5 = .6 4/5 = .8 1/6 = 2/6 = 3/6 = 4/6 = 5/6 = 1/7 = 2/7 = 3/7 = 4/7 = 5/7 = 6/7 = 1/8 = 2/8 = 3/8 = 4/8 = 5/8 = 6/8 = 7/8 = 1/9 = .111 1/10 = .1 2/9 = .222 . 2/10 = .2 3/9 = .333 3/10 = .3 4/9 = .444 4/10 = .4 5/9 = .555 5/10 = .5 6/9 = .666 6/10 = .6 7/9 = .777 7/10 = .7 8/9 = .888 8/10 = .8 9/10 = .9

9. Lesson 1: Terminating and Repeating Decimals 1/1 = 1.0 1/2 = .5 1/3 = .333 2/3 = .666 1/4 = .25 2/4 = .5 3/4 = .75 1/5 = .2 2/5 = .4 3/5 = .6 4/5 = .8 1/6 = 2/6 = 3/6 = 4/6 = 5/6 = 1/7 = 2/7 = 3/7 = 4/7 = 5/7 = 6/7 = 1/8 = .125 2/8 = .250 3/8 = .375 4/8 = .500 5/8 = .625 6/8 = .750 7/8 = .875 1/9 = .111 1/10 = .1 2/9 = .222 . 2/10 = .2 3/9 = .333 3/10 = .3 4/9 = .444 4/10 = .4 5/9 = .555 5/10 = .5 6/9 = .666 6/10 = .6 7/9 = .777 7/10 = .7 8/9 = .888 8/10 = .8 9/10 = .9

10. Lesson 1: Terminating and Repeating Decimals 1/1 = 1.02 1/2 = .5 1/3 = .333 2/3 = .666 1/4 = .25 2/4 = .5 3/4 = .75 1/5 = .2 2/5 = .4 3/5 = .6 4/5 = .8 1/6 = .1666.. 2/6 = .333 3/6 = .5 4/6 = .666 5/6 = .8333 . 1/7 = .142857 2/7 = .285714 3/7 = .428571 4/7 = .571428 5/7 = .714285 6/7 = .857142 1/8 = .125 2/8 = .250 3/8 = .375 4/8 = .500 5/8 = .625 6/8 = .750 7/8 = .875 1/9 = .111 1/10 = .1 2/9 = .222 . 2/10 = .2 3/9 = .333 3/10 = .3 4/9 = .444 4/10 = .4 5/9 = .555 5/10 = .5 6/9 = .666 6/10 = .6 7/9 = .777 7/10 = .7 8/9 = .888 8/10 = .8 9/10 = .9

11. Lesson 1: Terminating and Repeating Decimals Any fraction can be expressed as a decimal by dividing the numerator by the denominator. Example 1: If the repeating digit is zero, the decimal is a terminating decimal. 1 = .5 1 = .25 2 4 1 = .2 5 1 = .125 8

12. Lesson 1: Terminating and Repeating Decimals Example 2: If the repeating digit is not zero, the decimal is a repeating decimal. 1 = .3333 . .3 2 = .2222 .. 3 9 .2 1= .166666 .. .16 2 = .285714 6 7

13. Lesson 1: Terminating and Repeating Decimals If denominator is a factor of 10, 100, 1000 there is no need to use division. Words Fraction Decimal Seven tenths Nineteen hundredths One-hundred five thousandths

14. Lesson 1: Terminating and Repeating Decimals Words Fraction Decimal Seven tenths 7/10 .7 Nineteen hundredths 19/100 .19 One-hundred five thousandths 105/1000 .105

15. Lesson 1: Terminating and Repeating Decimals If denominator is a factor of 9, 99, 999 there is no need to use division. Words Fraction Decimal Five ninths Twelve ninety-nine hundredths One-hundred three nine hundred ninety-nine thousandths

16. Lesson 1: Terminating and Repeating Decimals If denominator is a factor of 9, 99, 999 there is no need to use division. Words Fraction Decimal Five ninths 5/9 .5 Twelve ninety-nine hundredths 12/99 .12 One-hundred three nine hundred ninety-nine thousandths 103/999 .103

17. Lesson 1: Terminating and Repeating Decimals Write the fraction or mixed number as a decimal. 1. 10 3 4 2. 5 7 3. 20 3 4. 5 4 6 5. 1 25

18. Lesson 1: Terminating and Repeating Decimals 3 6. 4 17 7. 1000 3 8. -6 5 3 9. 12 50 31 10. 10000

19. Lesson 1: Terminating and Repeating Decimals 11. 8 5 7 12. 16 3 13. 32 1 14. - 40 3 15. 80

20. Lesson 1: Terminating and Repeating Decimals 1. 3 2 7 2. 9 8 3. - 11 5 4. 33 12 5. 99

21. Lesson 1: Terminating and Repeating Decimals 6. _1_ 12 7. 3 7 8. _2_ 15

22. Lesson 1: Terminating and Repeating Decimals Write each terminating decimal as a fraction in simplest form. 1. .4 2. .35 3. -1.08 4. 8.625 5. -.6

23. Lesson 1: Terminating and Repeating Decimals Write each repeating decimal as a fraction in simplest form. 1. .77777777 2. .45454545 3. .125125125 . 4. .166666 . 5. .5833333 .

24. Real-World Problem There are .15 goldfish and .4 angelfish in the aquarium. Write the fraction that represents how many goldfish and angelfish are in the aquarium.

25. Classwork Guided Practice #1-5 Independent Practice #1-17 Problem Solving Practice # 1- 6

26. Closure Question: What number do you use in the denominator when writing terminating and repeating decimals to fractions? Exit Ticket Homework: Practice #1 -26

27. Exit Ticket Write each fraction as a decimal. 1. 18 25 2. 7 9 Write each decimal as a fraction. 3. .23 4. .4

28. Homework