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  4. Number of cyphers after decimal before a significant figure starts in ((5/2))-50 is [Use: log 10 2=0.3010 ]

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Q. Number of cyphers after decimal before a significant figure starts in $\left(\frac{5}{2}\right)^{-50}$ is [Use : $\log _{10} 2=0.3010$ ]

Continuity and Differentiability

Solution:

$\text { Let } N =\left(\frac{5}{2}\right)^{-50} $
$\Rightarrow \log _{10} N =-50 \cdot \log _{10}\left(\frac{5}{2}\right)=-50\left(\log _{10}\left(\frac{10}{2}\right)-\log _{10} 2\right)=-50\left(1-2 \log _{10} 2\right) $
$=-50(1-2 \times 0.3010)=-50(1-0.6020)=-50 \times 0.3980=-19 \cdot 9=-20+0.1=\overline{20} .10$
$\therefore \text { Number of zeroes }=19 $