SP#6: Unit K Concept 10 - Writing Repeating Decimals as Rational Numbers

Make sure to pay special attention to plug in the right numbers into the right formula. Since we'll be solving this without using a calculator, leave the numbers as fractions so they are easily simplified. Remember to add the fraction with the number in front of the decimal and to always check to see if your answer can be reduced.

Problem:
3.215215215215

1. Break apart each repeating unit. Ignore number in front of decimal for now. Arrange them into a geometric series.

2. Find the first term and the ratio. Keep them as fractions. (To find the common ratio, take any term and divide it by the preceding term.)

3. Use summation notation and plug in the numbers.

4. Plug into the infinite sum formula (a sub 1 divided by 1 minus r).

5. Simplify without a calculator. Multiply by the reciprocal to get rid of fraction in the denominator.

6. Check to see if resulting fraction can be reduced.

7. Bring back the number in front of decimal (3) and add it to the fraction. 

8. Can check answer by plugging in answer into calculator. Should end up with the number we started with.