Uncertainty for a ratio ( help)

• MitsuShai
In summary, the conversation discusses finding the uncertainty in the ratio of the diameter to thickness of a chocolate chip cookie. The formula for the ratio is d/h, and the method to solve it using calculus error propagation and partial derivatives is mentioned. However, this method is deemed confusing and the individual is unable to understand how to get a ratio from the partial derivative formula. They also mention trying to manipulate the volume formula, but are unable to find a solution. After spending a lot of time on the problem, the individual eventually figures it out.
MitsuShai
Uncertainty for a ratio (urgent help!)

Question: As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of d = 8.32 cm +/-1×10−2 cm and a thickness of h = 9.3×10−2 cm +/-1×10−3 cm.
Find the uncertainty in this ratio of the diameter to the thickness.

Hint:Notice the division.
If we are dividing that is a negative exponent.

The ratio of the diameter to the thickness is 89.5. How can I use the calculus error prop./the partial derivative to solve this? The hint also made things more confusing.
Someone said to said it up like this or something: d*h^-1, but I still don't understand.
Plus, I don't see how you can get a ratio from the partial derivative formula. And I tried manipulating the volume formula: v=[(pi d^2)/4]*h, but it can't go to d/h...I was spending my time yesterday and today just to solve this problem and I couldn't figure it out and it was the only problem I had trouble with...sorry I'm very frusterated right now >:[

Last edited:

nevermind I figured it out :)

What is uncertainty for a ratio?

Uncertainty for a ratio is a measure of the potential error or variability in a ratio calculation. It takes into account the uncertainty in the individual values used to calculate the ratio and provides a range within which the true value of the ratio is likely to fall.

How is uncertainty for a ratio calculated?

To calculate uncertainty for a ratio, the uncertainties in the individual values used to calculate the ratio must first be determined. These uncertainties are then combined using the formula for error propagation, which takes into account the mathematical relationship between the values. The result is a combined uncertainty for the ratio.

Why is uncertainty for a ratio important?

Uncertainty for a ratio is important because it provides a measure of the reliability or accuracy of a ratio calculation. It allows scientists to understand the potential error in their results and communicate this information to others. Additionally, uncertainty for a ratio is necessary for performing further statistical analyses on the data.

What factors can affect uncertainty for a ratio?

The uncertainty for a ratio can be affected by a number of factors, such as the precision and accuracy of the measurement instruments used, the variability of the individual values, and the mathematical relationship between the values. In some cases, external factors such as environmental conditions or human error may also contribute to uncertainty.

How can uncertainty for a ratio be reduced?

There are a few ways to reduce uncertainty for a ratio. First, using more precise and accurate measurement instruments can help decrease the uncertainty of the individual values. Additionally, reducing variability in the values used to calculate the ratio can also decrease overall uncertainty. When possible, increasing the sample size and performing multiple measurements can also help reduce uncertainty for a ratio.

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