Answer:
2. Tenths place
Explanation:
When you're concerned with the precision of a sum, the final value must be rounded to the precision of the least-precise contributor.
Precision
The numbers contributing to this sum are ...
7.273, with least significant digit in the thousandth's place.
-12.4, with least significant digit in the tenths place.
The smaller the place value of the least significant digit of a number, the greater the precision it has. The least-precise number will have the largest place value of its least-significant digit.
tenths > thousandths, so -12.4 has less precision
Sum
First of all, we compute the sum as though every contributor were exact. This is especially important when there are more than two contributors. With only two contributors, you get the same result if you round the more precise number first.
7.273 -12.4 = -5.127 . . . . . preferred method of finding the sum
7.3 -12.4 = -5.1 . . . . . . . . . . alternate approach for 2 contributors
Finally, we round that sum to the nearest tenth, reflecting the precision of -12.4:
sum = -5.1
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Additional comment
As a general rule, this fixation on precision applies to quantities that are measured, estimated, or rounded.
For example, it doesn't make much sense to report a financial value to the penny if one of the contributors has already been rounded to the nearest hundred-thousand dollars. The amount could already be in error by up to $50,000, so precision to the penny is meaningless.
When working many kinds of problems, it can be useful to report answers to the same precision used for the problem values. In some cases, you are told exactly what precision to use for an answer (nearest integer, tenth, or hundredth). Where you are not told, it usually doesn't make much sense to use 6 significant digits for an answer to a problem with values given as one significant digit. However, it can be sensible to report the answer to 2 or 3 significant digits.
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Here (in this problem), we're concerned with a sum. When you are computing a product or ratio, the rules are different. In those cases, the (least) number of significant digits in the contributors will determine the number of significant digits in the answer. Where mixed arithmetic (products and sums) is involved, the rounding of the final answer will depend on the final operation:
a(b+c) . . . the final operation is multiplication
ab +ac . . . the final operation is addition
As with all computation, the intermediate results should be carried to full calculator precision (unless directed otherwise). Only the final answer should be rounded to the necessary precision.