Question

The number of zeroes coming immediately after the decimal point in the value of$(0.2{)}^{25}$ is
(Note: ${\log }_{10}2=0.30103$)

• A. $16$
• B. $17$
• C. $18$
• D. none of these

Answer 1

The correct option is B $17$

Let, $y=(0.2{)}^{25}$
Taking log both sides on base 10.
$\Rightarrow {\log }_{10}y=25{\log }_{10}0.2$
$\Rightarrow {\log }_{10}y=25({\log }_{10}2-1)$
$\Rightarrow y={10}^{-25}{10}^{25{\log }_{10}2}={10}^{-25}{10}^{25\left(0.3013\right)}$
$\Rightarrow y={10}^{-17.4675}$
Ans: B