Question

The number of zeros between the decimal point and first significant digit of ${\left(0.036\right)}^{16}$ where $log2=0.301$ and $log3=0.477$

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

Answer 1

The correct option is C $23$

$y=(0.036{)}^{16}$

$\Rightarrow \log \left(y\right)=16log\left(0.036\right)$

$\Rightarrow \log \left(y\right)=16\log \left(\frac{36}{1000}\right)=16[\log 36-3{\log }_{10}10]$

$\Rightarrow \log \left(y\right)=16\left[\log \right(2^2\times 3^2)-3]=16\left[2\right(\log 2+\log 3)-3]$

$\Rightarrow \log \left(y\right)=16\left[2\right(0.301+0.477)-3]=-23.104<-23$

So, that number has $23$ zeros after this point.