Write whether the rational number $\frac{11}{125}$ will have a terminating decimal expansion or a non terminating repeating decimal expansion.

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Solution

If the denominator can be in the powers of either $2$ or $5$ or both, then it will be a terminating decimal, otherwise non-terminating.
Now, the denominator $125 = 5^{3}$ , i.e. is in the form $2^{m} \times 5^{n}$ ; where $n, m$ are non-negative.
Hence, the rational number has terminating decimal expansion.

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Write whether the rational number 11125 will have a terminating decimal expansion or a non terminating repeating decimal expansion.

If the denominator can be in the powers of either 2 or 5 or both, then it will be a terminating decimal, otherwise non-terminating.Now, the denominator 125=53, i.e. is in the form 2m×5n; where n,m are non-negative.Hence, the rational number has terminating decimal expansion.

Write whether the rational number $\frac{11}{125}$ will have a terminating decimal expansion or a non terminating repeating decimal expansion.