Question

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

• A. $15$
• B. $20$
• C. $17$
• D. $18$

Answer 1

The correct option is C $17$

Let $x=7^{-20}$
Then ${\log }_{10}x=-20{\log }_{10}7$
$=-20\times \left(0.8451\right)=-16.9020$
$\Rightarrow {\log }_{10}x=-17+1-0.9020=-17+0.0980$

$\therefore$ Characteristic $=-17$
Hence, position of the first significant figure is $17$th.