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  • Write the denominator of the rational number 257by5000 in the form 2power m × 5power n, where m, n are non-negative integers. Hence, write its decimal expansion, without actual division.

Write the denominator of the rational number 257/5000 in the form 2m × 5n, where m, n are non-negative integers. Hence, write its decimal expansion, without actual division.

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best_answer

Here, denominator = 5000
It can be written as:
5000 = 2 × 2 × 2 × 5 × 5 × 5 × 5
Hence the given fraction \frac{257}{2^{3}\times 5^{4}} can be written as:
   \Rightarrow \frac{257}{\left ( 2^{3}\times 5^{4} \right )5^{1}}
\Rightarrow \frac{257}{1000\times 5^{1}}\times \frac{2^{1}}{2^{1}}  (On dividing & multiply by 21)
\Rightarrow \frac{514}{10000}
\Rightarrow 0\cdot 0514
Hence, it is a terminating decimal.

Posted by

infoexpert27

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