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Geometric Series - Problem 11 312 views

If a decimal has one term that repeats infinitely, you can write that decimal as a fraction using the formula for an infinite geometric series. First, you need to re-write the decimal as a series by writing out each term being added to the next. Here, if only one digit repeats, you'll be adding one zero each time in front of the digit. Your r value is the ratio of a term to the one previous- in this case, if only one digit repeats, r will be 1 /10. From there, use the formula for an infinite geometric series to write your fraction, and then reduce it by multiplying by the reciprocal of the denominator. Check your work on a calculator using the f - > d or d - > f command.

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