Question

6) After how many decimal places will the decimal expansion of

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

terminate ?

Answer 1

We know that if the denominator of the rational number is of the form 2^n * 5^m, then it will terminate after n places(n > m) (or) after m places(m > n).

Given :

⇒ (23/2^4 * 5^3)

Here, n = 4, m = 3.

n > m.

Therefore, it will terminate after 4 decimal places.

Hope it helps!