Question

After how many places of decimal, will the decimal expansion of the rational number \(\frac {57}{2^4 5^6}\) terminate?

(a) 4

(b) 6

(c) 7

(d) 8

I got this question in an interview for internship.

The doubt is from Irrational and Rational Numbers in chapter Real Numbers of Mathematics – Class 10

Answer 1

The correct option is (b) 6

Easy explanation: We have,

\(\frac {57}{2^4 5^6} = \frac {57 \times 2^2}{2^6 5^6} = \frac {228}{10^6}\) = 0.000228

The number \(\frac {57}{2^4 5^6}\) will terminate after 6 decimal places.