1. Section 2.7 Terminating and Repeating Decimals

2. Section 2-7 When you divide decimals your answer will either be a terminating decimal or a repeating decimal. When you divide decimals your answer will either be a terminating decimal or a repeating decimal.

3. Terminating decimal When you divide decimals, if the quotient (the answer) stops it is a terminating decimal. When you divide decimals, if the quotient (the answer) stops it is a terminating decimal. Example: 3 divided by 4 = 0.75 Example: 3 divided by 4 = 0.75 The quotient 0.75 stopped it terminated, therefore it is a terminating decimal. The quotient 0.75 stopped it terminated, therefore it is a terminating decimal.

4. Repeating decimal When you divided decimals, if the quotient keeps repeating it is a repeating decimal. When you divided decimals, if the quotient keeps repeating it is a repeating decimal. Example: 1 dividing by 3= 0.3333333….. Example: 1 dividing by 3= 0.3333333….. You write the quotient as 0.3 with a bar over the 3! Not just 0.3 VERY IMPORTANT You write the quotient as 0.3 with a bar over the 3! Not just 0.3 VERY IMPORTANT

5. Why 0.3 with a bar over it and not 3??? 0.3 (bar over) 0.3 (bar over) Compare these numbers—which is bigger? Compare these numbers—which is bigger? 0.3 0.3

6. Circles, computers, and “Star Trek” are all linked to one number, pi or defines the relationship between a circle and its diameter. Circles, computers, and “Star Trek” are all linked to one number, pi or defines the relationship between a circle and its diameter. The numerical value of π truncated to 50 decimal places is: The numerical value of π truncated to 50 decimal places is:truncated decimal placestruncated decimal places –3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 While the value of pi has been computed to billions of digits, practical science and engineering will rarely require more than 10 decimal places. While the value of pi has been computed to billions of digits, practical science and engineering will rarely require more than 10 decimal places.

7. Pi Pi In 1767 Johann Lambert proved that pi is a decimal that neither terminates nor repeats. (It is called an irrational number) In 1767 Johann Lambert proved that pi is a decimal that neither terminates nor repeats. (It is called an irrational number)

8. Another cool fact: The number 142857 is called “roundabout.” The number 142857 is called “roundabout.” Check what happens when it’s multiplied by 2. Check what happens when it’s multiplied by 2. How about 3? How about 3? How about 7? How about 7?

9. Overview of Section 2.7 Terminating decimal – is Terminating decimal – is Repeating decimal – is Repeating decimal – is How do you write a repeating decimal? How do you write a repeating decimal?

10. Assignment Assignment Worksheet Worksheet Due tomorrow! Due tomorrow!