Math CentralQuandaries & Queries


Question from Clara, a student:

For which values of k will k/240 be a terminating decimal?

Hi Clara.

If you factor k/240, you can get this:

k/240 = k x (1/5 x 1/2 x 1/2 x 1/2 x 1/2 x 1/3)

A terminating decimal times any other terminating decimal always equals a terminating decimal.

Since 1/5 and 1/2 are terminating decimals, I know that (1/5 x 1/2 x 1/2 x 1/2 x 1/2 x 1/3) = 1/80 is a terminating decimal.

Clearly, k is an integer, so that terminates. Thus k/80 must be a terminating decimal.

This leaves just the question then of when k/80 x 1/3 is a terminating decimal.

Can you finish the problem now?

Stephen La Rocque.

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