Question

The number of decimal places after which the decimal expansion of the rational number 14588/625 will terminate is=

Answer 1

$\frac{14588}{625} = \frac{14588}{ {5}^{4} } \\ = \frac{14588 \times {2}^{4} }{ {5}^{4} \times {2}^{4} } \\ = \frac{14588 \times 16}{ {10}^{4} } \\ = \frac{233408}{ {10}^{4} } \\ = 23.3408$
hence this rational number will terminate after 4 decimal places.
answer:-4
hope this will help