# What would my uncertainty be with these 2 values?

• nukeman
In summary, to calculate the percent difference between two values, you can use the formula p(a,b) = (b - a)/b * 100. To determine the error in this function, you can use the partial derivatives of the function with respect to each variable and calculate the sum of their squares multiplied by the corresponding errors. This method can be applied to functions with any number of variables.
nukeman

## Homework Statement

I am doing percent difference of 2 values.

value 1 = .013329 +- .001 cm
value 2 = .013331 +- .001 cm

So, for percent difference I do:

.013331 - .013329 / ((.013331 + .013329)/2)

gives me .015%, but what would my uncertainty be? I don't wuite understand. Thanks!

## The Attempt at a Solution

I believe when you divide or multiply numbers, the uncertainly is the sum of the uncertainty in your original numbers.

Percent difference between two values a and b can be written as a function of the two variables a and b:

##p(a,b) = \frac{b - a}{b}100##

If its variables have independent associated errors Δa and Δb, then the error in the function, Δp, can be obtained using partial derivatives of the function w.r.t. those variables, so that:

## \Delta p^2 = \left| \frac{\partial p}{\partial a}\right|^2 \Delta a^2 + \left| \frac{\partial p}{\partial b}\right|^2 \Delta b^2##

You can do the same for functions of any number of variables, f(a,b,c,...). All you need to be able to do is take partial derivatives of the function w.r.t. each of its variables.

## What is uncertainty?

Uncertainty refers to the amount of doubt or lack of precision in a measurement or value. It is often expressed as a range of possible values rather than a single, definitive number.

## How is uncertainty calculated?

Uncertainty is typically calculated using statistical methods, such as standard deviation or confidence intervals. These calculations take into account the variability and potential sources of error in the data or measurements.

## What factors affect uncertainty?

Uncertainty can be affected by a variety of factors, including the precision and accuracy of the measurement instruments, the skill and technique of the person making the measurement, and any sources of error or variability in the data.

## Why is it important to consider uncertainty?

Considering uncertainty is important because it helps us understand the limitations and potential errors in our measurements and data. It also allows us to make informed decisions and draw accurate conclusions based on our findings.

## Can uncertainty be completely eliminated?

No, uncertainty cannot be completely eliminated. Even with the most precise and accurate measurement techniques, there will always be some level of uncertainty due to the inherent variability and limitations in our measurements and data.

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