Write whether the rational number $\frac{64}{455}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion

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Solution

$\frac{64}{455}$ can be written as below

$\frac{64}{455} = \frac{64}{5 \times 7 \times 13}$

Clearly the denominator, 455 is not in the form of $2^{m} \times 5^{n}$ .
So the decimal expansion of $\frac{64}{455}$ is non terminating repeating.

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Without actually performing the long division, state whether the following rational number will have a terminating or a non-terminating repeating decimal expansion.

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Question 1 (iii)
Without actually performing the long division, state whether $\frac{64}{455}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 1 (iii)
Without actually performing the long division, state whether $\frac{64}{455}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Q. Question 1 (iii)
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\frac{64}{455}

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Write whether the rational number 64455 will have a terminating decimal expansion or a non-terminating repeating decimal expansion

64455 can be written as below64455=645×7×13Clearly the denominator, 455 is not in the form of 2m×5n.So the decimal expansion of 64455 is non terminating repeating.

Write whether the rational number $\frac{64}{455}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion

$\frac{64}{455}$ can be written as below

$\frac{64}{455} = \frac{64}{5 \times 7 \times 13}$

Clearly the denominator, 455 is not in the form of $2^{m} \times 5^{n}$ .
So the decimal expansion of $\frac{64}{455}$ is non terminating repeating.