Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{35}{50}$

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Solution

On simplifying, the denominator $10 = 2 \times 5 = 2^{1} {.5}^{1}$
Therefore, denominator is of the form $2^{n} {.5}^{m}$ , where m=1 and n=1.
It means rational number $\frac{35}{50}$ has 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 : 3550

On simplifying, the denominator 10=2×5=21.51 Therefore, denominator is of the form 2n.5m, where m=1 and n=1. It means rational number 3550 has 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 : $\frac{35}{50}$

On simplifying, the denominator $10 = 2 \times 5 = 2^{1} {.5}^{1}$
Therefore, denominator is of the form $2^{n} {.5}^{m}$ , where m=1 and n=1.
It means rational number $\frac{35}{50}$ has terminating decimal expansion.