Which of the following is/are true ?

Options

A. number of digits in `8^(12)5^(35)` is 35
B. number of digits in `8^(12)5^(35)` is 36
C. number of zeroes after decimal before a significant figures starts in `((8)/(27))^(20)` is 10
D. number of zeroes after decimal before a significant figure starts in `((8)/(27))^(20)` is 11

Answer

B, C

Explanation

Let `N_(1)=8^(12)5^(35)`
`rArr log_(10)N_(1)=log_(10)(2^(36).5^(35))`
`log_(10)(10^(35).2)`
`=35+log_(10)2`
`=35+0.3010`
`= 35.3010`
`therefore` Number of digits in `N_(1)` is 36.
Now, let `N_(2)=((8)/(27))^(20)`
`rArr log_(10)N_(2)=20 log_(10)((8)/(27))`
`=60 "log"_(10)(2)/(3)`
`=60(log_(10)2-log_(10)3)`
`=60xx(0.3010-0.4771)`
`=-60xx(0.3010-0.4771)`
`-60xx0.1761`
`=-10.56`
`=bar(11)+0.44`
`therefore` Number of zeroes after decimal before a significant figure starts in `N_(2)` is 10