Question

Number of zeros after decimal before first significant digit in the number $(0.\overline{3}{)}^{10000}$ is (approximate value of ${\log }_{10}3$ is $0.4771$)

• A. $4770$
• B. $4771$
• C. $4772$
• D. $4773$

Answer 1

The correct option is B $4771$

Number of zeros after decimal in $(0.3{)}^{10000}$.

A number $x$ satisfies ${10}^{-n}\le x\le {10}^{-n+1}$, if and only if $-n\le {\log }_{10}x\le -n+1$

$\Rightarrow {\log }_{10}{3}^{-10000}=-10000{\log }_{10}3=-4771.2<{\log }_{10}x<-4770.2$

Number of zeros after decimal $=4771$