Question

If log₁₀2 = 0.3010.log₁₀3 = 0.4771 then the number of ciphers after decimal before a significant figure comes in `(5/3)^-100` is ______.

Options

• 21

• 22

• 23

• 24

Answer 1

If log₁₀2 = 0.3010.log₁₀3 = 0.4771 then the number of ciphers after decimal before a significant figure comes in `(5/3)^-100` is 22.

Explanation:

N = `(5/3)^-100`

⇒ log₁₀N = –100(log5 – log3)

= –100(1 – 0.3010 – 0.4771)

= –100(0.2219)

= –22.19

= –23 + 0.81

Characteristic = –23

⇒ Number of ciphers after the decimal (22).