1. 5 Minute Check

10. Mid C

13. Thursday, April 23 Lesson 7.4.1 Terminating and Repeating Decimals

14. Objective: To write fractions as terminating or repeating decimals and write decimals as fractions.

15. Terminating and Repeating Decimals A Rational Number is any number that can be written as a fraction. That means it can be written as a fraction, in which both the numerator and the denominator are whole numbers.

16. Terminating and Repeating Decimals

17. Non-rational numbers are called irrational numbers. Do you know an irrational number?

18. Terminating and Repeating Decimals What if you had a square with an area of 2u². What are the lengths of the sides?

19. Terminating and Repeating Decimals What if you had a square with an area of 2u². What are the lengths of the sides? x · x = 2 or x² = 2 √x² = √2 x = √2 = 1.4142135………… √2 is also an irrational number!

20. Terminating and Repeating Decimals Every rational number can be written as either a terminating decimal or repeating decimal. What is the difference between terminating and repeating?

21. Terminating and Repeating Decimals Every rational number can be written as either a terminating decimal or repeating decimal. Bar notation is a bar placed over the digit(s) that repeat. e.g. 0.54545454… = 0.54

22. Terminating and Repeating Decimals 5 Write 12 as a decimal. How do you set this up as a math problem?

23. Terminating and Repeating Decimals 5 Write 12 as a decimal. 12 ) 5 or 5 ÷ 12 How do we do this?

24. Terminating and Repeating Decimals 5 Write 12 as a decimal. 12 ) 5.000 Place the decimal point and annex zeros.

25. Terminating and Repeating Decimals 5 Write 12 as a decimal. 0.4166 12 ) 5.0000 -48 20 -12 80 -72 80 -72 8 Why can I stop dividing ?

26. Terminating and Repeating Decimals 5 Write 12 as a decimal. 0.4166 12 ) 5.0000 -48 20 -12 80 -72 80 -72 8

27. Terminating and Repeating Decimals 5 Write 12 as a decimal. 0.416

28. Terminating and Repeating Decimals 1 Write 6 as a decimal. Do this on your own.

29. Terminating and Repeating Decimals 1 Write 6 as a decimal. 0.16 0.166 6)1.000 -6 40 -36 40

30. Terminating and Repeating Decimals

46. Write -2.4 as a fraction. Do this on your own.

47. Terminating and Repeating Decimals Write -2.4 as a fraction. 4 2 -2.4 = -2 10 = -2 5 Remember – When converting a decimal to a fraction, say the fraction in word form, write it down and simplify.

48. Terminating and Repeating Decimals Frank made 34 out of 44 free throws this season. What is his free throw percentage? Do this on your own.

49. Terminating and Repeating Decimals Frank made 34 out of 44 free throws this season. What is his free throw percentage? 00.7727 Here is the decimal, what is the percentage? 44 )34.00000 -308 320 -308 120 -88 320 -308 120

50. Terminating and Repeating Decimals Frank made 34 out of 44 free throws this season. What is his free throw percentage? 00.7727 Here is the decimal, what is the percentage? 44 )34.00000 -308 320 -308 120 -88 320 -308 120 77.27%

51. Terminating and Repeating Decimals Suppose you buy a 1.25 pound package of ham at $5.20 per pound. What fraction of a pound did you buy?

52. Terminating and Repeating Decimals

55. Write a fraction and an equivalent terminating decimal between 0.5 and 0.75.

56. Terminating and Repeating Decimals Write a fraction and an equivalent terminating decimal between 0.5 and 0.75. Sample answer: 3 5 = 0.6

57. Terminating and Repeating Decimals Fractions in simplest form that have denominators of 2, 4, 8, 16, and 32 produce terminating decimals. Fractions with denominators of 6, 12, 18,and 24 produce repeating decimals. What causes the difference?

58. Terminating and Repeating Decimals Fractions in simplest form that have denominators of 2, 4, 8, 16, and 32 produce terminating decimals. Fractions with denominators of 6, 12, 18,and 24 produce repeating decimals. What causes the difference? The first set can be factored into primes of 2’s. The second set can be factor into primes of 2’s and 3’s. The factor of 3 produces the repeating decimal.

59. Terminating and Repeating Decimals

62. Agenda Notes No Homework – Homework Practice 7.4.1 Odd Numbers Only. Due by the end of the period Circle all answers and show all work. Mid-Chapter 7.4 Quiz Thursday, April 30