Dividing a number w/uncert by a number w/o uncert

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This results in the final answer having an uncertainty of 0.1. This follows the general rule that when dividing by a constant, the numerical value of the uncertainty remains the same, but the units change accordingly. In summary, when dividing a number with an uncertainty by a constant, the uncertainty is also divided by the constant to determine the uncertainty of the final answer.
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Homework Statement


If I have a number with an uncertainty and I want to divide it by a number without an uncertainty (ex. if it's just a constant, like pi), what do I do with the uncertainty? Is it ok to just divide the uncertainty by that number?

ex. (4.05 +/- 0.3) / 3

Do I divide the 0.3 uncertainty by 3, and that would be my uncertainty for the final answer, or do I have to do percentage uncertainties?

Homework Equations


N/A

The Attempt at a Solution


Intuition tells me it's the first, but I'm not sure.
 
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  • #2
(4.05 +/- 0.3) / 3 = (4.08 to 4.02) / 3 = 1.36 to 1.34 = 1.35 +/- 0.1

So I think you are right.
 
  • #3
Yes, the uncertainty is also mulitplied (or divided, in this case) by the constant.
 

What does it mean to divide a number with uncertainty by a number without uncertainty?

Dividing a number with uncertainty by a number without uncertainty is a mathematical operation used to determine the ratio between two quantities when one of the quantities has a known margin of error or uncertainty. This is commonly used in scientific experiments and data analysis.

Why is it important to account for uncertainty when dividing numbers?

Accounting for uncertainty when dividing numbers is important because it allows for a more accurate representation of the data. When there is uncertainty in one of the numbers being divided, it can affect the overall accuracy of the result. By incorporating uncertainty into the calculation, we can better understand the reliability of the data and make more informed conclusions.

How do you perform division with uncertainty?

To perform division with uncertainty, you must first determine the uncertainty of each number involved in the calculation. Then, you divide the numbers as you normally would, but instead of reporting a single result, you report the result as a range with the uncertainty included. This is typically done by using significant figures.

Can uncertainty affect the result of a division?

Yes, uncertainty can definitely affect the result of a division. When dividing a number with uncertainty, the uncertainty is propagated through the calculation and can result in a larger uncertainty in the final result. Therefore, it is important to consider uncertainty when interpreting the results of a division.

What are some common sources of uncertainty when dividing numbers?

There are several sources of uncertainty when dividing numbers, including measurement errors, rounding errors, and limitations of measurement instruments. Other factors such as human error, environmental conditions, and systematic errors can also contribute to uncertainty when dividing numbers. It is important to identify and account for these sources of uncertainty to ensure the accuracy of the calculations.

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