Which one of the following has a terminating decimal expansion?

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\frac{5}{32}

\frac{7}{9}

\frac{8}{15}

\frac{1}{12}

answer is A.

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Detailed Solution

Given,

\frac{5}{32}

\frac{7}{9}

\frac{8}{15}

and

\frac{1}{12}

.
We know that a terminating decimal is a decimal that ends. It has a decimal with a finite number of digits. For example

\frac{1}{4} = 0.25

, it has only two decimal digits.
Now considering the fraction

\frac{5}{32}

whose decimal form will be:

\frac{5}{32} = 0.15625

The resulting decimal number ends with five decimal digits and therefore, it is terminating decimal.
Hence,

\frac{5}{32}

has a terminating decimal expansion.
While,

\frac{7}{9} = 0.7777 . . .

, non-terminating,

\frac{8}{15} = 0.5333 . . .

, non-terminating and

\frac{7}{9} = 0.08333 . . .

, non-terminating.
Therefore, option (1) is correct.

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