Question

Number of cyphers after decimal before a significant figure starts in $\left(\frac{3}{2}\right)^{-100}$, is [Given: $\log _{10} 2=0.3010$ and $\log _{10} 3=0.4771$ ]

• A. 16
• B. 17
• C. 18
• D. 19

Answer 1

Answer: (B)

Let $N =\left(\frac{3}{2}\right)^{-100}$
$\therefore \log N=100[\log 3-\log 2]=-100[0.4771-0.3010]=-100 \times 0.1761=-17.61$
$\therefore$ Number of cyphers after decimal before a significant figure starts in $\left(\frac{3}{2}\right)^{-100}$, is $|-18|-1=17$