Question

If P is non negative characteristics of $lo{g}_{10}N$, then number of significant digit in N is $P+1$. If $-P$ is the negative characteristics of $lo{g}_{10}N$, then the number of zeros after decimal before a significant digit start are $P-1$ (Use $lo{g}_{10}2=0.3010,lo{g}_{10}3=0.4771$) On the bases of the above information, answer the following:

Number of significant digit in N, where $N=(\frac{5}{3}{)}^{100},$ is

• A. 23
• B. 22
• C. 21
• D. None of these

Answer 1

Answer: (A)

23

Given $N={\left(\frac{5}{3}\right)}^{100}$

Hence,

$\log N=100\left(\log \frac{5}{3}\right)=100(\log 5-\log 3)=100(\log \frac{10}{2}-\log 3)=100(1-0.301-0.4771)=22.19$

Hence number of significant digits$=P+1=22+1=23$