Without actual division, state whether the following rational numbers will have terminating or non-terminating decimal representation.

a) $\frac{64}{455}$ b) $\frac{13}{3125}$

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Solution

For a terminating decimal, denominator must be in the form of $2^{m} 5^{n}$

a) $\frac{64}{455}$ = $\frac{64}{5 \times 7 \times 13}$ ; It is clearly not in the form of $2^{m} 5^{n}$
So, it is non–terminating.
b) $\frac{13}{3125}$ = $\frac{13}{2^{0} 5^{5}}$ ; It is in the formof 2^m5ⁿ
So, it is terminating.

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Question 1 (i)
Without actually performing the long division, state whether $\frac{13}{3125}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

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

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Without actual division, state whether the following rational numbers will have terminating or non-terminating decimal representation. a) 64455 b) 133125

For a terminating decimal, denominator must be in the form of 2m5n​​ a) 64455 = 645×7×13; It is clearly not in the form of 2m5n So, it is non–terminating. b) 133125 = 132055 ; It is in the formof 2m5n So, it is terminating.

Without actual division, state whether the following rational numbers will have terminating or non-terminating decimal representation.

a) $\frac{64}{455}$ b) $\frac{13}{3125}$