Question

Given, ${\log }_{10}2=0.3010,{\log }_{10}3=0.4771$. The number of zeros after the decimal in $3^{-100}$ are

• A. $140$
• B. $47$
• C. $12$
• D. none of these

Answer 1

Answer: (B)

$47$

Let $y=3^{-100}$
Take log on both side on base 10,
${\log }_{10}y=-100{\log }_{10}3=-100\times .4771=-47.71$
Hence, number of zeros after decimal is 47.