Without actually performing the long division- state whether 6-15 will have a terminating decimal expansion or a non-terminating repeating decimal expansion-

6/15 On dividing the numerator and the denominator by 3; we get 2/5. Here, denominator is in the form of 2^m× 5^n, where m = 0 and n = 1. nbsp; Thus, the deci ...

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Standard IX

Mathematics

Real Numbers

Without actua...

Question

Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

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Solution

$\frac{6}{15}$
On dividing the numerator and the denominator by 3; we get $\frac{2}{5}$ .
Here, denominator is in the form of $2^{m} \times 5^{n}$ , where m = 0 and n = 1.
Thus, the decimal expansion of the number $\frac{6}{15}$ is terminating.

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Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

$\frac{6}{15}$
On dividing the numerator and the denominator by 3; we get $\frac{2}{5}$ .
Here, denominator is in the form of $2^{m} \times 5^{n}$ , where m = 0 and n = 1.
Thus, the decimal expansion of the number $\frac{6}{15}$ is terminating.