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

If \[\frac{13}{125}\]is a rational number, then decimal expansion of it, 'which terminates

A) 0.104

B) 1.04

C) 0.0104

D) 0.140

Correct Answer: A

Solution :

Given rational number is \[\frac{13}{125}\]

\[\therefore\] Prime factorisation of \[125={{5}^{3}}\]

Now, \[\frac{13}{125}=\frac{13}{{{5}^{3}}}=\frac{13\times {{2}^{3}}}{{{5}^{3}}\times {{2}^{3}}}=\frac{104}{{{10}^{3}}}=0.104\]

[make the denominator in the power of 10]

Thus, \[\frac{13}{125}\] has decimal expansion, which terminates.