1. Converting Fractions to Decimals & Repeating Decimals
Monday, September 8th and Tuesday, September 9th
Students will be able to convert fractions to decimals and understand the concept behind converting repeating decimals fractions.

2. Non-terminating repeating decimal numbers are all . . . RATIONAL
We talked how terminating decimal numbers are obviously rational numbers.
How about non-terminating decimal numbers?

3. Converting Fractions
 Take for example 1/9 and convert it into a decimal number with long division algorithm.  What do you get?  
How about 2/9?  3/9?  1/11?  2/13?  7/15?  Can you find more fractions that turn into non-terminating decimal numbers?

4. Converting Fractions
Since = 1/9, then the decimal number is a rational number.  
In fact, every non-terminating decimal number that REPEATS a certain pattern of digits, is a rational number.  

5. Converting Fractions
For example, let's make up a decimal number that never ends.  
Do you believe we CAN write it as a fraction, in the form a/b?
(This sounds like it would be pure guesswork, but no, there is a method, a nice and clever one).

6. Converting Fractions - Example
Let's name our number a = and multiply it by a power of 10, then subtract the original a and the new number so that the repeating decimal parts cancel each other in the subtraction.
Follow with me….

7. Example Write down the original number as… a = 0.135135135...
Now, multiply both sides by a =
Now, multiply both sides by a =
Now, multiply both sides by a =
This will work, the decimals line up now

8. Example (cont) Then we subtract the original from the 1000a.
Write the equation a =
Now subtract the original a =
999a = 135
Now, divide both sides by 999, which will result in: a = 135/999