Final answer:
When adding or subtracting numbers, round the result to the precision of the least precise number. For multiplication or division, match the number of significant figures to the least precise term. For addition of numbers with different signs, use subtraction and affix the sign of the larger value.
Step-by-step explanation:
When performing arithmetic operations such as addition or subtraction, the precision of the result is dependent on the number with the least precision. This is typically represented by the number with the least number of decimal places. For instance, if you have two measurements, 78,500 m and 362 m, when subtracted, the raw result is 78,138 m. However, since the first measurement is only precise to the hundreds place, the final answer should be rounded to the same level of precision, which in this case is 78,100 m. Similarly, in operations like multiplication or division, the final answer should have the same number of significant figures as the measurement with the fewest significant figures.
It is advisable to maintain two extra significant figures during intermediate steps in a multi-step calculation and only apply the rules of significant figures when arriving at the final answer. Doing so can increase the accuracy of the results. Remember, when dealing with positive numbers in addition, the result is positive, and when adding two negative numbers, the result is also negative. When numbers of opposite signs are added together, one must subtract the smaller number from the larger and affix the sign of the larger number.