CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
Given log 2 = 0.3010, how many digits are there in the integral part of 2^40?
2^40 has 13 digits. Its logarithm is 40 times 0.3010, which is 12.04, giving a characteristic of 12. The number of digits in the integral part is the characteristic plus one, so 13. Taking 12 digits would be forgetting that rule.
- A11
- B12Correct
- C13
- D14
Explanation
log 2^40 = 40 × 0.3010 = 12.04. The characteristic is 12, so the number of digits is characteristic + 1 = 13. Option 12 wrongly equates digits with the characteristic.
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