Question

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

Answer 1

Denominator of `257/5000` is `5000`.
`5000 = 5**10**10**10 = 5**5**2**5**2**5**2 = 2^3xx5^4`
Here, `m = 3 and n = 4`
Now, `257/5000 = 257/5000**2/2 = 514/10000 = 0.0514`, which is the required decimal expansion.