How many digits in 2⁴⁰ — Number System Aptitude Question
How many digits in 2⁴⁰: How many digits are there in 2⁴⁰? (Take log₁₀2 = 0.3010.) Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
How many digits are there in 2⁴⁰? (Take log₁₀2 = 0.3010.)
Options
- 12
- 13
- 14
- 15
Show the answer and the worked solution
Correct answer: B. 13
Worked solution
- log₁₀(2⁴⁰) = 40 × 0.3010 = 12.04.
- Number of digits = ⌊12.04⌋ + 1 = 12 + 1 = 13.
Answer: 13.
The idea
Digits of N = ⌊log₁₀N⌋ + 1. The integer part tells you the power of ten; the +1 is the leading digit itself. Forgetting the +1 gives 12, which is offered.
Shortcut. 2¹⁰ = 1024 ≈ 10³, so 2⁴⁰ = 1024⁴ ≈ 1.1 × 10¹², a number with 13 digits.
Common trap. 12 — the integer part of 12.04 taken as the digit count, missing the +1 for the leading digit.