10th Class Mathematics Real Numbers Question Bank MCQs - Real Numbers

The decimal expansion of \[\frac{23}{{{2}^{5}}\times {{5}^{2}}}\] will terminate after how many places of decimal? (CBSE 2020)

A) 2

B) 4

C) 5

D) 1

Correct Answer: C

Solution :

Sol. [c] \[\frac{23}{{{2}^{5}}\times {{5}^{2}}}=\frac{23}{{{2}^{5}}\times {{5}^{2}}}\times \frac{{{5}^{3}}}{{{5}^{3}}}\]

\[=\frac{23\times 125}{{{(2\times 5)}^{5}}}=\frac{2875}{100000}=0.02875\]

\[\therefore \] The decimal expansion will terminate after 5 places of decimal.