How are uncertainties combined in multiplication and division?

In multiplication and division, uncertainties are combined by adding the percentage uncertainties of the quantities involved.

When you're dealing with multiplication or division of quantities in physics, it's important to understand how to combine the uncertainties of those quantities. This is done by adding the percentage uncertainties of each quantity. The percentage uncertainty of a quantity is the absolute uncertainty divided by the value of the quantity, multiplied by 100%.

For example, let's say you're multiplying two quantities A and B, where A has a value of 10 with an uncertainty of ±1, and B has a value of 5 with an uncertainty of ±0.5. The percentage uncertainty of A is (1/10)*100% = 10%, and the percentage uncertainty of B is (0.5/5)*100% = 10%. When you multiply A and B, the percentage uncertainty of the result is the sum of the percentage uncertainties of A and B, which is 10% + 10% = 20%.

The same principle applies when you're dividing two quantities. If you're dividing A by B, the percentage uncertainty of the result is again the sum of the percentage uncertainties of A and B.

This method of combining uncertainties is based on the assumption that the uncertainties are small compared to the values of the quantities, and that they are random and independent of each other. If these conditions are not met, a more complex method of combining uncertainties may be needed.

IB Physics Tutor Summary: In summary, when multiplying or dividing quantities in physics, combine their uncertainties by adding their percentage uncertainties together. This involves calculating each quantity's percentage uncertainty (absolute uncertainty divided by the quantity's value, times 100%) and adding these percentages. This method assumes uncertainties are small, random, and independent. If not, a more complex approach is needed.