Final answer:
In mathematical operations, for addition and subtraction round off to the least number of decimal places, while for multiplication and division round off to the least number of significant figures. Always retain precision through intermediate steps and round only the final answer to prevent rounding errors.
Step-by-step explanation:
When performing calculations involving both addition/subtraction and multiplication/division, it's essential to follow specific rounding rules to ensure the accuracy of your final answer. For addition and subtraction, the rule is to round the result to the same number of decimal places as that of the number with the least number of decimal places. This ensures that the precision of the least precise measurement is not exceeded. For example, when we add 13.2 and 12.252, our answer 25.452 should be rounded to 25.5 to maintain one decimal place.
In multiplication and division, the final answer should be rounded to the same number of significant figures as the measurement with the fewest significant figures. For example, multiplying 1.35 by 2.1 results in 2.835, which should be rounded to 2.8 to match the least number of significant figures, which in this case is two.
It's also important to minimize rounding errors by carrying as many digits as possible through intermediate steps of the calculation, rounding only the final answer to the required precision. If intermediate rounding is absolutely necessary, you should keep at least one more digit than the final rounding requirement.
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