Sig Fig Problem: Calculating t with I=3.20A, L=4.2m, etc

  • Thread starter Tcat
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In summary, significant figures are important in scientific calculations as they indicate the precision of a measurement or calculation. To determine the number of significant figures, count all non-zero digits and any zeros between them. Rounding off significant figures is allowed but should be done carefully to maintain accuracy. Significant figures also affect the precision of scientific results and it is essential to use the correct number of significant figures to ensure accuracy in data analysis.
  • #1
Tcat
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In this one problem I am given I=3.20A, L=4.2m, cross-section=.00220m, n=8.85*10^28, and e=1.6*10^-19.
I am using an equation that is set up like this to find the t=((l*w)*n*q*L)/I
When I calculate ((0.00220m)^2*(8.85*10^28)(1.6*10^-19)*(4.2))/(3.2) I get 8.99*10^4 and for some reason the sig. figs are wrong! I don't know why?
 
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  • #2
Since L and e are given only to two significant figures your final answer should also be written to two significant figures.
 
  • #3


It appears that the incorrect number of significant figures is due to rounding errors in the calculation. When rounding each individual term in the equation to the correct number of significant figures, the final answer should be 8.99*10^4 seconds, or 89,900 seconds. However, it is always important to double check your calculations and make sure that you are using the correct number of significant figures throughout the entire equation to avoid any errors. Additionally, it may be helpful to show your work and include units in your calculations to ensure accuracy.
 

1. What are significant figures and why are they important in scientific calculations?

Significant figures, also known as significant digits, are the digits in a number that are considered to be accurate and reliable. They indicate the precision of a measurement or calculation and are important in scientific calculations to ensure accuracy and consistency in data analysis.

2. How do I determine the number of significant figures in a given measurement or calculation?

To determine the number of significant figures in a measurement, count all non-zero digits and any zeros between them. Trailing zeros after a decimal point are also significant. In calculations, the result should have the same number of significant figures as the measurement with the least number of significant figures.

3. Can I round off significant figures in scientific calculations?

Yes, significant figures can be rounded off in scientific calculations to match the precision of the measurement. The general rule is that when rounding off, the last digit should be increased by 1 if the next digit is 5 or higher, and left unchanged if the next digit is 4 or lower.

4. How do I apply significant figures in the formula for calculating t with I=3.20A, L=4.2m, etc?

In this formula, the values for I and L have three and two significant figures respectively. Therefore, the answer should also have two significant figures. When plugging in the values, be sure to use the full, unrounded values to avoid rounding errors in the calculation.

5. Can significant figures affect the precision of scientific results?

Yes, significant figures play an important role in determining the precision of scientific results. Rounding off or using too few significant figures in calculations can lead to inaccurate results. It is important to use the correct number of significant figures to maintain precision and accuracy in scientific calculations.

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