Question

After how many decimals place will the decimals expansion of $\frac{23}{2^4\times 5^3}$ terminate?

Answer 1

$\frac{23}{2^4\times 5^3}$

$=\frac{23}{2^4\times 5^3}\times \frac{5}{5}$

$=\frac{23\times 5}{2^4\times 5^4}$

$=\frac{105}{{(2\times 5)}^4}$

$=\frac{105}{{10}^4}=\frac{105}{10000}=0.0105$

So,after $4$ decimal places, the number will terminate.