Question

If ${\log }_{10}7=0.8451$ then the position of the first significant figure of $7^{-20}$ is

• A. $16$
• B. $17$
• C. $20$
• D. $15$

Answer 1

The correct option is B $17$

${\log }_{10}\left(7\right)=0.8451$. Hence taking logarithm of $7^{-20}$ implies

Let $x=7^{-20}$

${\log }_{10}x={\log }_{10}{7}^{-20}$
$=-20{\log }_{10}\left(7\right)$
$=-20\left(0.8451\right)$
$=-2\left(8.451\right)$
$=-16.92$ which lies between $-17$ and $-16$
Thus the position of the first significant figure is $17$.