1. Converting Repeating Decimals to Fractions

2. This Gets a Little Complex As we go through a few examples, I want you to look for patterns.

3. Multiplying by a power of 10 What happens to my decimal any number every time I multiply by ten? – Start with the number 8.0

4. What About This 0.0034

5. Repeating Decimals We need to get the entire portion of the decimal that repeats to the left side of the decimal place To do this we will multiply each side by a power of ten until this is accomplished

6. Repeating Decimals Lets look at 0.4 We will make x = 0.4 If I multiply both sides by 10 I get: 10x = 4.4 which can break into 10x = 4 + 0.4 x = 0.4 so I can substitute 10x = 4 + (x) Now I need to get one of the variables isolated 10x – x = 4 + x – x therefore 9x = 4

7. 0.818181……. Let x = 0.81 100x = 81.81 or 100x = 81 + 0.81 100x = 81 + x 100x – x = 81 + x – x therefore 99x = 81

8. 0.234234234….. x = 0.234 1000x = 234.234 or 1000x = 234 + 0.234 1000x = 234 + x 1000x – x = 234 + x – x therefore 999x = 234

9. Do You See the Pattern? Can you do this mentally yet? – What is the fractional equivalent of 0.434343….?

10. Why might it be important to be able to convert a repeating decimal to a fraction?

11. Exit Find the fractional equivalent: – 1) 0.77777….. – 2) 0.527527…… – 3) 0.91269126…….