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.

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