Mathematically, this doesn't make much sense. I get what you're trying to say, but R can't simultaneously be the sum, difference, product, and quotient of two values.Apashanka said:We define R=p+q,p-q,p/q,pq
Yes, I understand that, but IMO R=p+q,p-q,p/q,pq is an abuse of notation where there is no explanation that this is shorthand.mathman said:Mark44: I believe the question is for .four cases.
When adding or subtracting errors, you simply add or subtract the values of the errors. For example, if you have an error of ±2 and you add it to another error of ±3, the resulting error would be ±5.
The rule for multiplying or dividing errors is to calculate the relative error for each individual measurement, and then add the relative errors together to get the overall relative error. For example, if you have a measurement with an error of ±5% and another measurement with an error of ±3%, the resulting error after multiplication would be ±8%.
No, you cannot multiply or divide errors with different units. Before performing any calculations, you must convert all errors to the same units. This ensures that the errors are consistent and can be accurately combined.
Absolute error is the difference between the measured value and the true value, while relative error is the absolute error divided by the true value. Relative error is often expressed as a percentage, while absolute error is expressed in the same units as the measured value.
When performing a series of calculations, it is important to carry the error through each step and combine them using the rules for addition, subtraction, multiplication, and division of errors. This ensures that the final result has an accurate error range that takes into account all previous calculations.