# Fractional uncertainty and propagation of uncertainties

• quietrain
In summary, when a value with uncertainty, such as y = 10 ± 3, is multiplied by a constant, the uncertainty also scales. This means that if y is multiplied by 2, the new value becomes y = 20 ± 6. Similarly, when dividing by a constant, the uncertainty also scales. Understanding this concept is important in calculating fractional uncertainty and propagating uncertainties.
quietrain
erm, ok let's say i have a value, with uncertainty, like y = 10 ± 3

so let's say i multiply y by 2, then it becomes 20

but does the uncertainty becomes 3 x 2 = 6? , hence y = 20±6 ?

what about divide? does it becomes 1.5?

i roughly understand fractional uncertainty and propagation of uncertainties, but what if i multiply the value of y with a constant as in the case above. what will become of the uncertainty?

thanks for help!

Yes, in that case the uncertainty scales.

Think about it this way - if you know the radius of a circle is 10 ± 3, you don't know the diameter any better than ± 6, right?

ah i see thanks a lot!

## 1. What is fractional uncertainty?

Fractional uncertainty is a measure of the relative uncertainty or error associated with a particular measurement. It is typically expressed as a percentage or decimal value.

## 2. How is fractional uncertainty calculated?

Fractional uncertainty is calculated by dividing the absolute uncertainty by the measured value and multiplying by 100 to get a percentage. This can also be expressed as a decimal value by dividing the absolute uncertainty by the measured value.

## 3. What is the purpose of propagating uncertainties?

Propagating uncertainties involves calculating the uncertainty of a final result based on the uncertainties of the individual measurements used to obtain that result. This is important because it allows us to understand the overall uncertainty associated with a calculation or experiment.

## 4. How is uncertainty propagated in calculations?

Uncertainty is propagated in calculations by using the rules of uncertainty propagation, which involve adding or subtracting uncertainties when combining measurements, and multiplying or dividing uncertainties when using mathematical operations. These rules are based on the principle of error propagation.

## 5. How can fractional uncertainties affect the reliability of results?

Fractional uncertainties can affect the reliability of results by indicating the level of confidence we can have in the accuracy of a measurement. The higher the fractional uncertainty, the less reliable the result is likely to be. It is important to keep uncertainties as low as possible through careful measurement and appropriate use of uncertainty propagation techniques.

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