CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
Given log10(3) = 0.4771, the value of log10(0.0003) is written in the bar form as:
log10(0.0003) = 4̄.4771. Writing 0.0003 as 3 × 10^-4 gives a characteristic of -4, with the mantissa the same as for 3, namely 0.4771. The characteristic is negative one more than the count of zeros after the decimal point.
- A4̄.4771Correct
- B3̄.4771
- C3.4771
- D2̄.4771
Explanation
0.0003 = 3 × 10^-4, so log = -4 + 0.4771 = 4̄.4771. The characteristic is -4, and the mantissa stays positive at 0.4771. Option 3̄.4771 wrongly counts only three places (the number of zeros after the decimal point is 3, so the characteristic is -(3+1)).
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