Question

Number of cyphers after decimal before a significant figure comes in ${\left(\begin{array}{c}\frac{5}{3}\end{array}\right)}^{-100}$ is
Note: ${\log }_{10}5=0.6990,{\log }_{10}3=0.4770$.

• A. $21$
• B. $22$
• C. $23$
• D. $24$

Answer 1

Answer: (B)

$22$

$x={\left(\begin{array}{c}\frac{5}{3}\end{array}\right)}^{-100}\Rightarrow {\log }_{10}x=-100(\log 5-\log 3)$
$=-100({\log }_{10}10-{\log }_{10}2-{\log }_{10}3)$
$=-100(1-.3010-.4771)$
$=-22.19$
Hence, no. of cyphers is $=22$