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# Characterization of Repeating and Terminating Decimals

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a. Which fractions a/b have terminating decimals?

b. Which fractions a/b have repeating decimals?

c. Sometimes (for example 1/12 ) only part of the decimal repeats while in other cases (for example 1/7 ) the whole decimal repeats. Assuming a/b is a reduced fraction, how can you tell which of these two scenarios will occur? Explain.

*d.* Marcus says he computed and found

0.0588235294

Josie looks at this answer for a second or two and tells Marcus that he is mistaken. Josie did NOT calculate any of the numbers in this decimal. How might Josie have known Marcusâ?? calculation is incorrect?

https://brainmass.com/math/fractions-and-percentages/characterization-repeating-terminating-decimals-426904

## SOLUTION This solution is FREE courtesy of BrainMass!

a. Fractions with terminating decimals are fractions in which the only primes dividing the denominators (when reduced) are 2 and 5.

b. All other fractions have repeating decimals.

c. The whole decimal repeats precisely when the denominator is a factor of 10^n-1, where n is the period of repetition. In particular, if the denominator is even (as it is for 1/12), only part of the decimal repeats.

d. I don't understand what this question is asking for. What is Marcus computing? If he is computing the decimal expansion of 1/17, he is correct up to the number of places he has calculated. However, if this is his final answer, the fraction must have been 294117647/5000000000, which is unlikely.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!