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Q.
Find the number of naughts after decimal before a significant figure comes in the number $\left(\frac{5}{6}\right)^{100}$.
Continuity and Differentiability
Solution:
$ y =\left(\frac{5}{6}\right)^{100} \Rightarrow \log _{10} y =100\left(\log _{10} 5-\log _{10} 6\right)=100\left(1-\log _{10} 2-\log _{10} 3-\log _{10} 2\right) $
$\Rightarrow -7.91 \Rightarrow-8+0.09$
since char is -8 . Hence number of zeros after decimal $=7$