Without doing any actual division, find which of the following rational number have terminating decimal representation:
$\frac{17}{40}$ .

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Solution

Given, $\frac{17}{40}$ .
Since the denominator $40 = 2 \times 2 \times 2 \times 5 = 2^{3} \times 5^{1}$ ,
i.e. $40$ can be expressed as $2^{m} \times 5^{n}$ .
Therefore, $\frac{17}{40}$ will have a terminating decimal expansion.

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Similar questions

Q. Without doing any actual division, find which of the following rational numbers have terminating decimal representation :
(i)

\frac{7}{16}

(ii)

\frac{23}{125}

(iii)

\frac{9}{14}

(iv)

\frac{32}{45}

(v)

\frac{43}{50}

(vi)

\frac{17}{40}

(vii)

\frac{61}{75}

(viii)

\frac{123}{250}

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(ii)

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Without doing any actual division, find which of the following rational number have terminating decimal representation:1740.

Given, 1740.Since the denominator 40=2×2×2×5=23×51,i.e. 40 can be expressed as 2m×5n.Therefore, 1740 will have a terminating decimal expansion.

Without doing any actual division, find which of the following rational number have terminating decimal representation:
$\frac{17}{40}$ .

Given, $\frac{17}{40}$ .
Since the denominator $40 = 2 \times 2 \times 2 \times 5 = 2^{3} \times 5^{1}$ ,
i.e. $40$ can be expressed as $2^{m} \times 5^{n}$ .
Therefore, $\frac{17}{40}$ will have a terminating decimal expansion.