Discussion
What is the value of the sum of 12.1100 +18.0 +1.012 as per the rule of significant figures?
Answer: D
The sum, rounded correctly, is 31.1.
In addition and subtraction the result keeps as many decimal places as the least precise number. Here 12.1100 has four decimal places, 18.0 has one and 1.012 has three, so the answer may carry only one decimal place.
\[ \begin{aligned} 12.1100 + 18.0 + 1.012 &= 31.1220 \\ &\approx 31.1 \end{aligned} \]
31.1220 and 31.122 report precision that 18.0 does not have, and 31.12 keeps one decimal place too many. 31 drops a decimal place that 18.0 does justify. The rule about counting significant figures applies to multiplication and division, not to sums.
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