Question

The number of zeros coming immediately after the decimal point in the value of $(0.2{)}^{25}$ is
(Given ${\log }_{10}2=0.3010)$

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

Answer 1

The correct option is B $17$

Let $x=(0.2{)}^{25}$
Then ${\log }_{10}x=25{\log }_{10}0.2$
$\Rightarrow {\log }_{10}x=25{\log }_{10}\left(\frac{2}{10}\right)$
$\Rightarrow {\log }_{10}x=25({\log }_{10}2-1)$
$\Rightarrow {\log }_{10}x=25\times 0.3010-25\Rightarrow {\log }_{10}x=7.525-25\Rightarrow {\log }_{10}x=-18+0.525$

Hence, there are $|-18+1|=17$ zeros immediately after the decimal point.