Without actually performing the long division- state whether77-210 will have a terminating decimal expansion or a non-terminating repeating decimal expansion-

77/210 Simplify it by dividing nbsp;numerator nbsp;and denominator by 7 to get 11/30. On factorising the denominator, we get; 30=2 × 3 × 5 The denominator i ...

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Standard IX

Mathematics

Natural Numbers

Without actua...

Question

Without actually performing the long division, state whether $\frac{77}{210}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

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Solution

$\frac{77}{210}$
Simplify it by dividing numerator and denominator by 7 to get $\frac{11}{30}$ .
On factorising the denominator, we get;
$30 = 2 \times 3 \times 5$
The denominator is not in the form of $2^{m} \times 5^{n}$ .
Hence, the decimal expansion of $\frac{77}{210}$ is non terminating repeating.

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Without actually performing the long division, state whether77210 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

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