Transforming Simple Repeating Decimals to Fractions and Vice Versa – Practice Problems

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When you learned about fractions and decimals, you may have noticed that some fractions such one-half, one-fourth, one-eighth, and so on divided out to nice terminating decimals such as 0.50, 0.25, 0.125, and so on. The decimals terminated meaning they ended or stopped.

Other fractions such as 1/3, 1/6, and 1/9 - when you used long division to divide out these numbers to make their equivalent decimals, the remainder just went on and on… repeating over and over, and you indicated the repeating digits with a horizontal bar placed above the repeating digits. Problem solved. But, for repeating decimals, how do you go in the other direction, from decimal to fraction? How do you deal with the repeating digits? What happens to that extra little piece – is it just lost forever?

To change from a repeating decimal into a fraction, there is a trick, and it involves the number 9. Put the repeating number or numbers in the numerator then put the same number of 9s in the denominator and simplify. To see this trick in action and figure out what to do with numbers that go on and on and on, so you can switch from fraction to decimal and back again, watch this video.

Apply and extend previous understandings of operations with fractions. CCSS.MATH.CONTENT.7.NS.A.1

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Exercises in this Practice Problem
Explain how to divide 100 dollars evenly between three people.
Define a repeating decimal.
Decide how much money each band member should receive.
Write repeating decimals as fractions.
Convert the fraction $\frac13$ into a decimal by using long division.
Determine the repeating decimal equivalent for each given fraction and vice versa.