Question

The number of zeroes coming immediately after the decimal point in the value of `(0.2)^25` is : Given `log_10 2 = 0.30103`)
A. 16
B. 17
C. 18
D. none of these

Answer 1

Correct Answer - B
Let `x = (0.2)^(25)`. Then,
`"log"_(10)x = 25 "log"_(10)0.2`
`rArr "log"_(10) x = 25 ("log"_(10) 2-1)`
`rArr "log"_(10) = 25 xx 0.30103 - 25 = -18 + 0.52575`
Hence, there are 17 zeros immediately after the decimal point.