Write the denominator of rational number


Write the denominator of rational number $\frac{257}{5000}$ in the form $2^{m} \times 5^{n}$, where $m, n$ are non-negative integers.

Hence, write its decimal expansion, without actual division


Denominator of the rational number $\frac{257}{5000}$ is 5000 .

Now, factors of $5000=2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5=(2)^{3} \times(5)^{4}$, which is of the type $2^{m} \times 5^{n}$,

where $m=3$ and $n=4$ are non-negative integers.

$\therefore \quad$ Rational number $=\frac{257}{5000}=\frac{257}{2^{3} \times 5^{4}} \times \frac{2}{2}$

[since, multiplying numerator and denominater by 2]

$=\frac{514}{2^{4} \times 5^{4}}=\frac{514}{(10)^{4}}$


Hence, which is the required decimal expansion of the rational $\frac{257}{5000}$ and it is also a 5000 terminating decimal number.

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