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Write the denominator of the rational number \(\frac{257}{5000}\) in the form 2m × 5n, where m, n are non-negative integers. Hence, write the decimal expansion, without actual division.

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The denominator of the given rational number is 5000. 

⇒ 5000 = 23 x 54 

It’s seen that, 23 x 54 is of the form 2m x 5n, where m = 3 and n = 4. 

\(\frac{257}{5000}\)

= \(\frac{(257\, \times\, 2)}{(5000\, \times\, 2)}\)

= \(\frac{514}{10000}\)

= 0.0514 is its decimal expansion.

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