Can subtracting reduce the number of Significant Figures a number has?

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ColmConnolly3D
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Can subtracting reduce the number of Significant Figures a number has?

Postby ColmConnolly3D » Mon Jan 25, 2021 4:42 pm

Say I have to subtract then divide:

0.7552g - 0.7241g = 0.0311 g <- Here we keep 4 decimal places because we are subtracting.

For my next step, I would like to divide by 768.95 g/mol

Will my rounded answer be 4.044*10^-5 mol or 4.04*10^-5 mol? The question boils down to can subtraction reduce the accuracy of a measurement. Since the subtraction answer came from two numbers with 4 sf accuracy, why would subtracting them (which only cares about the # of places after a decimal) decrease its accuracy to 3 sf? Should I just stick to the original sf accuracy in this situation since the calculations are separate steps, or rather reevaluate the sig figs the number has after my first step.

This question pertains to my lab for 14BL, but I have changed the numbers around so you aren't doing the work for me :)

Hoping someone can help!
Colm

Chloe Little 3K
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Re: Can subtracting reduce the number of Significant Figures a number has?

Postby Chloe Little 3K » Mon Jan 25, 2021 5:25 pm

Your rounded answer should have 4 sig figs which would be 4.044*10^-5 mol because when you divide, the number of significant figures in the answer should match the number of significant figures of the least precisely known number used in the calculation, meaning the number with the fewest sig figs. Since 0.0311 g has 4 sig figs and 768.95 g/mol has 5 sig figs, your answer should have 4 sig figs.

Allison Peng 1F
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Re: Can subtracting reduce the number of Significant Figures a number has?

Postby Allison Peng 1F » Mon Sep 27, 2021 11:50 am

I would say that the final answer should have three significant figures. After you do the subtraction, you keep the number of digits past the decimal place, and that can change the number of significant figures (for example, 0.0311 has three significant digits, not four; therefore, after you multiply or do anything with the 0.0311 number, the resulting answer will have 3 significant figures as well).

Srikar_Chintala_1A
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Re: Can subtracting reduce the number of Significant Figures a number has?

Postby Srikar_Chintala_1A » Mon Sep 27, 2021 12:04 pm

Subtraction should not reduce the number of sig figs a number has. Since both the numbers being used in subtraction have four sig figs, the answer should also have four sig figs. This means the answer should be 0.03110. Now, when you divide this number by 768.95, you want to use the lowest amount of sig figs based on the numbers you have. In this case, it would be 4 again since 768.95 has 5 sig figs. That means your answer should be 4.044*10^-5 mol.

Ashley M 1F
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Re: Can subtracting reduce the number of Significant Figures a number has?

Postby Ashley M 1F » Mon Sep 27, 2021 2:56 pm

When adding or subtracting, the number of significant figures your answer has depends on the number with the least amount of decimal places. Thus, after subtracting, your answer should have 4 decimal places, and therefore 4 significant figures. However, after multiplying or dividing, you should round your answer to the same number of significant figures as the measurement with the fewest significant figures. In your case, the previous answer achieved from subtracting had 4 significant figures, which is fewer than the other value that has 5 significant figures. This means your final answer should have 4 significant figures.


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