Question

What the number of decimal places after which the decimal expansion of rational number 14588 by 625 will terminate?

Answer 1

14588/625===>>23.3408

It is terminating after 4 digits

Answer 2

At first, let us represent the denominator in form of $2^a . 5^b$. The $max(a, b)$ will be the answer.

$\dfrac{14588}{625} = \dfrac{14588}{2^0 . 5^4}$.

⇒ $max(0, 4) = 4$.

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