# Solving Percentage Errors: Different Magnitudes for Positive & Negative

• lavster
In summary, the conversation discusses how to get positive and negative errors to be different in magnitude. It is explained that this can be seen in examples such as calculating the error of the area of an annulus from two circular areas. The conversation also touches on the concept of asymmetric uncertainties and how they can occur in measurements and mathematical analysis.
lavster
How can you get positive and negative errors to be different in magnitude?

for example -

when calculating the error of the area of an annulus from two circular areas (ie subtracting one from the other, why is the positive error greater than the negative error

Thanks

because the denominators are different...

like, say, you have $100 invested and you lose$20...that's a $20 loss... Now you have$80...What percentage gain do you need to get your \$20 back...
20/80 is 25%.

figures don't lie, but liars figure!

i understand the money analogy, but not when talking about the areas - sorry! :S we are only subtracting once

lavster said:
i understand the money analogy, but not when talking about the areas - sorry! :S we are only subtracting once

Could you illustrate by an example what you are concerned about?

Imagine a square where both sides are known with a precision of 10% - they might be 10% shorter or 10% longer, but not more. What is the maximal deviation?

Larger area: Both sides 10% longer, total area 1.1^2 = 1.21 of the original area (21% more).
Smaller area: Both sides 10% shorter, total area 0.9^2 = 0.81 of the original area (19% less).
Do you see the difference?

mfb said:
Imagine a square where both sides are known with a precision of 10% - they might be 10% shorter or 10% longer, but not more. What is the maximal deviation?

Larger area: Both sides 10% longer, total area 1.1^2 = 1.21 of the original area (21% more).
Smaller area: Both sides 10% shorter, total area 0.9^2 = 0.81 of the original area (19% less).
Do you see the difference?

I see the difference, but why do you see this as a problem?

The error depends on how the measurement was taken and what analysis was done. When you do math on the measurement, the errors will change shape. If you measure a circle's radius with a ruler with a symmetric error in the length, then the error in the area is not symmetric, because area goes as length squared.

mathman said:
I see the difference, but why do you see this as a problem?
Where did I say that it is a problem?
I just said that you can get asymmetric uncertainties in this way.

ah great :) thanks :)

## What is a percentage error?

A percentage error is a calculation used to determine the difference between a measured or estimated value and the actual value. It is expressed as a percentage and can be positive or negative.

## How do you calculate percentage error?

To calculate percentage error, you take the difference between the measured value and the actual value, divide it by the actual value, and then multiply by 100. The formula is: % error = (measured value - actual value) / actual value * 100.

## Why do we use different magnitudes for positive and negative percentage errors?

We use different magnitudes for positive and negative percentage errors because they represent different types of errors. A positive percentage error means that the measured value is higher than the actual value, while a negative percentage error means that the measured value is lower than the actual value. Using different magnitudes allows us to distinguish between these two types of errors.

## What is an acceptable range for percentage error?

The acceptable range for percentage error varies depending on the context and the specific application. In general, a percentage error of less than 5% is considered acceptable, but this may differ for different industries and fields of study.

## How can we minimize percentage error in scientific experiments?

To minimize percentage error in scientific experiments, it is important to use precise and accurate measurement tools, follow standardized procedures, and repeat experiments multiple times to ensure consistency. It is also important to understand and properly account for any sources of error in the experiment.

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