Retaining an Extra Significant Figure in Intermediate Steps of a Calculation

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Doubt

I am in class 11 I read in my physics textbook that if we are doing a multi-step calculation. Then we should retain an extra significant figure in the intermediate steps and in the final answer we should calculate the appropriate significant figures.

I am thinking in two different ways:

1) In first step when I multiply or divide, I must retain an extra significant figure. Then in the next step i perform multiplication and division and retain an extra significant figure, and so on. At last, I should perform multiplication or division and then do not retain an extra digit.

2) In first step after performing multiplication or division I should retain an extra digit then in intermediate steps I should not retain an extra digit. At last, in last step I should decrease a significant figure because I had included an extra digit in first step.

Which one is correct according to the concept of rounding off significant figures?


The correct approach is:

1) In the first step when you multiply or divide, you must retain an extra significant figure. Then in the next step you perform multiplication and division and retain an extra significant figure, and so on. At last you should perform multiplication or division and then do not retain an extra digit.

Here's why:

  • Intermediate steps: Retaining an extra significant figure in intermediate steps helps to minimize rounding errors that can accumulate as calculations progress. This ensures that the final answer is as accurate as possible.
  • Final answer: In the final answer, you should round off to the appropriate number of significant figures based on the least precise measurement used in the calculation. This is to avoid reporting a level of accuracy that is not supported by the original data.

By following this approach, you can ensure that your calculations are accurate and your results are presented with the appropriate level of precision.

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