Write the denominator of rational number $\frac{257}{5000}$ in the form $2^m \times5^n$,where $m, n$ are non-negative integers. Hence, write its decimal expansion, without actual division

AcademicMathematicsNCERTClass 10


The given rational number is $\frac{257}{5000}$.

To do: 

Here, we have to write the decimal expansion of the given rational number by writing its denominator in the form of $2^m \times 5^n$, where m, and n, are non-negative integers.



We can see that $2^3\times5^4$ is of the form $2^m \times 5^n$, where $m =3$ and $n = 4$.

This implies,

The given rational number has a terminating decimal expansion.

Multiply the numerator and denominator by $2^1$ so that the denominator becomes a multiple of $10^r$, where r is any positive integer. 







The decimal expansion of the given rational number is $0.0514$.

Updated on 10-Oct-2022 13:27:08