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Chapter 1: Problem 28

In a multiple-step calculation, is it better to round off the numbers to the correct number of significant figures in each step of the calculation or to round off only the final answer?

Short Answer

Expert verified
In a multiple-step calculation, it is generally better to round off only the final answer and keep the intermediate values with more significant figures to retain accuracy and avoid accumulated errors during the calculation process. This is because rounding off at each intermediate step can introduce insignificant errors in calculations, which might magnify in more complex problems with higher numbers of steps.

Step by step solution

01

Consider an example problem

Let's take an example of a multiple-step calculation to have a better understanding of the problem: Suppose we are given the following calculation: (3.42 * 7.107) + (1.97 / 5.65)
02

Step by step calculation without rounding off intermediate values

We'll perform the given calculation without rounding off the intermediate values: 1. (3.42 * 7.107) = 24.32574 2. (1.97 / 5.65) = 0.3486725663716814 3. Sum of the two values: 24.32574 + 0.3486725663716814 = 24.674412566371682 Now, we'll round off the final answer to the correct number of significant figures: In this case, the least significant figure in the given numbers is 2 so we have: Final answer: 24.67
03

Step by step calculation with rounding off intermediate values

Now, let's perform the calculation by rounding off the intermediate values to the correct number of significant figures: 1. (3.42 * 7.107) = 24.33 (rounded to 4 significant figures) 2. (1.97 / 5.65) = 0.3487 (rounded to 3 significant figures) 3. Sum of the two values: 24.33 + 0.3487 = 24.6787 Now, we'll round off the final answer to the correct number of significant figures: Final answer: 24.68
04

Compare the two approaches

Comparing the results of both methods, we can observe that the difference between the final answers obtained by using the two methods is small (24.67 vs 24.68). However, rounding off at each intermediate step can introduce insignificant errors in calculations, which might magnify in more complex problems with higher numbers of steps. So, it is generally better to round off only the final answer and keep the intermediate values with more significant figures to retain accuracy and avoid accumulated errors during the calculation process.

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