Question

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

Answer 1

The decimal expansion of the number $\frac{23}{2^4{.5}^3}$ will terminate after $4$ decimal places.

$\frac{23}{2^4{.5}^3}=\frac{23\times 5}{2^3{.5}^4}=\frac{115}{{10}^4}=0.0115$.

Hence, the decimal will terminate after $4$ decimal place.