Question

Number of zeros after decimal before a significant figure in $(75{)}^{-10}$ is (use ${\log }_{10}2=0.301$ and ${\log }_{10}3=0.477$ )

• A. 20
• B. 19
• C. 18
• D. none

Answer 1

Answer: (C)

$N=(75{)}^{-10}$
${\log }_{10}N=-10\log (75)$
$=-10\left[{\log }_{10}25+{\log }_{10}3\right]$
$=-10\left[2{\log }_{10}5+{\log }_{10}3\right]$
$=-10\left[2\left\{{\log }_{10}10-{\log }_{10}2\right\}+{\log }_{10}3\right]$
$=-10[2\{1-0.301\}+0.477]$
$=-10[0.699\times 2+0.477]$
$=-10[1.398+0.477]$
$=-10[1.875]\Rightarrow \text{ characteristic of }N=-19=p$
$=-18.75\Rightarrow \text{ Number of zeros after decimal }=|p|-1=|-19|-1=19-1=18$