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 the raitonal number `(257)/(5000) "is" 5000`.
Now, factors of 5000 `=2 xx 2xx 2xx 5xx 5xx 5xx 5=(2)^(3)`, which is of the type `2^(m)xx6(n)`, where m=3 and n=4 are non-negative integers
`therefore` Rational number `=(257)/(5000)=(257)/(2^(3)xx5^(4)xx(2)/(2)` [Since, multiplying numerator and denominator by 2]
`=(514)/(2^(4)xx5^(4))=0.00514`
Hence, which is the required decimal expansion of the rational `(257)/(5000)` and it is also terminating decimal number.