Which of the fractions listed below will have repeating decimals and which will have terminating decimals? explain how you know without doing any work!

Rule: if the denominator can be factored so that only 2 or 5 show up, and no other factor, then the fraction will turn into a terminating decimal.

For example: The fraction 1/5 = 0.2 is terminating. So is 1/10 = 0.1 and 1/20 = 0.05; all of the denominators can be factored to only have 2's or 5's as factors.

A nonexample would be 1/6 = 0.16666... where the 6's go on forever. The fact that the denominator 6 factors into 2*3 means that the rule above isn't satisfied.

With this in mind, we can say

2/5 = 0.4 is terminating (only 5 is a factor)

7/45 = 0.1555... is non-terminating because 45 has 3 as a factor

5/99 is the same story as 7/45 because 3 is a factor of 99

27/250 is terminating since 250 = 2*5*5*5 only has 2's or 5's as factors

i can answer this question sweetie!

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