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

Without actually performing the long division, the terminating decimal expansion of \[\frac{51}{1500}\]is in the form of \[\frac{17}{{{2}^{n}}\times {{5}^{m}}},\] then \[(m+n)\] is equal to:

A) 2

B) 3

C) 5

D) 8

Correct Answer: C

Solution :

Sol. [c] We have, \[\frac{51}{1500}=\frac{17}{500}\] Prime factorization of 500

\[=2\times 2\times 5\times 5\times 5={{2}^{2}}\times {{5}^{3}}\]

which is in the form \[{{2}^{n}}\times {{5}^{m}}\]

So, it has a terminating decimal expansion.

Now, \[\frac{51}{1500}=\frac{17}{{{2}^{2}}\times {{5}^{3}}}\]

By comparing, we get \[n=2\] and \[m=3\]

\[m+n=2+3=5\]