CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
If log10(x) = 3̄.5000, how many zeros come immediately after the decimal point in x before the first non-zero digit?
There are 2 zeros. A characteristic of 3̄ means x lies between 0.001 and 0.01, specifically x ≈ 0.00316. The number of zeros right after the decimal point equals the absolute value of the characteristic minus one, which is 2.
- A3
- B1
- C2Correct
- D4
Explanation
The characteristic 3̄ means -3, so x = 10^-3 × 10^0.5 ≈ 3.16 × 10^-3 = 0.00316. Here there are 2 zeros after the decimal point. The rule is zeros = |characteristic| - 1 = 3 - 1 = 2. Option 3 forgets to subtract 1.
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