Applying Sig Figs to Complex Calculations

  • Thread starter firstwave
  • Start date
In summary: Sirius' solution is correct, but the pedantic side of me insists I point out that the numerator of that expression has only two significant digits, despite being written as though it had eight. Since you don't really know what the digits are in the "52000" after the 2, adding the .042 makes no significant difference in the number.
  • #1
firstwave
12
0
I understand that if your doing multiplication, round to the least amount of sig figs. Addition: Round to the least amount of decimal places.

What about a question with both multiplication, division and addition, subtraction?

Such as

(5.2 x 10^4 + 4.2 x 10^-2)/ 3.6 x 10^2

How would I apply sig figs on that?

Thx in advance
 
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  • #2
[tex]\frac{52000+0.042}{360}=\frac{52000.042}{360}\approx 144.4445611\approx 144[/tex]

That is how I would do it. 3 significant digits in the 360, so the same for the answer, and don't round anything until the end.
 
  • #3
Sirus said:
[tex]\frac{52000+0.042}{360}=\frac{52000.042}{360}\approx 144.4445611\approx 144[/tex]

That is how I would do it. 3 significant digits in the 360, so the same for the answer, and don't round anything until the end.
I think it's about context too. If the question was about a length measurement taken (just say) and the value was 360mm, then shouldn't that should be taken to 2 sig.fig (unless they actually say it was measured to 3 sigfig)?
 
  • #4
I'm assuming the instrument used had millimeter markings. Good point, though.
 
  • #5
thx guys :D

I think 360 is 2 sig figs

360.0 = 4 sig figs
 
  • #6
firstwave said:
I think 360 is 2 sig figs
When written as in your first post (3.6 x 10^2) it has 2 sig figs for sure; 3 sig figs would be written as 3.60 x 10^2
 
  • #7
Oh boy, big mistake on my part. Corrected:

[tex]\frac{52000+0.042}{360}=\frac{52000.042}{360}\approx 144.4445611\approx 1.4\times{10^{2}}[/tex]

Firstwave, do the calculation, then look over to see the least number of significant digits in the original data. Sorry for misleading you earlier; my mistake.
 
  • #8
ok thanks all
 
  • #9
Sirus said:
Oh boy, big mistake on my part. Corrected:

[tex]\frac{52000+0.042}{360}=\frac{52000.042}{360}\approx 144.4445611\approx 1.4\times{10^{2}}[/tex]

Firstwave, do the calculation, then look over to see the least number of significant digits in the original data. Sorry for misleading you earlier; my mistake.

Sirius' solution is correct, but the pedantic side of me insists I point out that the numerator of that expression has only two significant digits, despite being written as though it had eight. Since you don't really know what the digits are in the "52000" after the 2, adding the .042 makes no significant difference in the number.
 

What are significant figures?

Significant figures are the digits in a number that represent the precision of the measurement. They include all digits that are known for certain, plus one estimated digit.

Why are significant figures important?

Significant figures are important because they indicate the level of precision of a measurement. They help communicate the accuracy of a measurement and are used in calculations to ensure the correct number of significant figures is maintained.

How do you determine the number of significant figures in a number?

The general rule for determining significant figures is to start counting from the leftmost non-zero digit and continue until the last digit. Zeros between non-zero digits and trailing zeros after a decimal point are also significant. Zeros at the beginning of a number are not significant unless they are to the right of a decimal point.

What is the purpose of rounding with significant figures?

Rounding with significant figures helps to maintain the appropriate level of precision in a calculated result. It ensures that the result is not more precise than the original data.

What are some common examples of when significant figures are used in science?

Significant figures are used in many scientific measurements and calculations, such as in chemistry experiments, physics experiments, and engineering designs. They are also used in data analysis and reporting of results in scientific research.

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