Review and Repeating Decimals

Hi guys. Let's review what we already know about converting decimals to fractions. Remember this step-by-step guide when you get stuck.

1) NAME the decimal (use your place value chart to find out what it "says").
    Example: .075 would be "seventy-five hundredths" since the last digit ends in the hundredths place
                   .6 would be "six tenths" because the number ends in the tenths place
                   1.457 would be "one and four hundred fifty-seven thousandths" because the last digit ends in the
                             thousandths place

2) Write your fraction. Let's use .075 as our example. Since we know .075 is "seventy-five hundredths", we write our fraction out as 75/100.

3) Reduce to simplest terms. 75/100 simplified would be 3/4 (remember, this is where we use the GCF to simplify)

Once you're able to turn decimals into fractions, all we need to do is use a little algebra to figure out how to turn those pesky repeating decimals into fractions. I'm not a big fan of the way your textbook explains it, so let me see if I can explain it in a simpler way.

Let's take the following number as an example (the same one in your textbook) - remember to click on the pictures to make them bigger:

1) Step one: Ignore the repeating symbol (pretend it's not even there). Move the decimal to the END of the number until it's a whole number.

2) Count how many times you moved your decimal to the right. In our case, it was TWO times.

3) Raise the number 10 to THAT power (the number of times you moved the decimal). In our case, we moved it TWO times, so we raise 10 to the second power:

4) Here comes the weird part. Subtract 1 from whatever number you got when you did step 3. In our case, we got 100. 100 - 1 = 99.

5) Now set up an equation that says "99x equals 72" (we are bringing back that "72" from when we moved the decimal in step 1).

6) Use what you already know about algebraic equations to solve for "x" by dividing both sides by 99.

7) We now have a fraction on the right side. Use the GCF (in this case, 9) to divide down and simplify your fraction.

So our answer is 8/11.



Here are the first two quick checks for this concept written out using our steps (sorry the second one is a little blurry):

I know it's tough but if you keep going through these steps and examples I know you'll get the hang of it. Try the third Quick Check as a class and let me know how it goes!