Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{17}{8}$

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Solution

$8 = 2 \times 2 \times 2 = 2^{3}$
Therefore, denominator is of the form $2^{n} {.5}^{m}$ , where m=0 and n=3.
It means rational number $\frac{17}{8}$ has a terminating decimal expansion.

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 178

8=2×2×2=23 Therefore, denominator is of the form 2n.5m, where m=0 and n=3. It means rational number 178 has a terminating decimal expansion.

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{17}{8}$

$8 = 2 \times 2 \times 2 = 2^{3}$
Therefore, denominator is of the form $2^{n} {.5}^{m}$ , where m=0 and n=3.
It means rational number $\frac{17}{8}$ has a terminating decimal expansion.