Error Propagation: Solutions to Complex Equations

[coregis]

Always the easy things we forget...
I know how errors propagate through multiplication or division when every term has an error, but how do I propagate errors in equations when only one term has an uncertainty? I want to say just multiply and divide the uncertainty value by the constants, i.e plug my value in the equation, then plug the uncertainty. This is the same as if I just found the % uncertainty, and multiplied the final product by that, correct? Is this the right way to go about this? And what if two (or more) terms have uncertainties? Would I find the uncertainty between those terms and then apply that % to the final number? Thanks.

 

[HallsofIvy]

If you mean something like y= ax+ b where a and b are exactly defined constants and x is measurement: x= m+/- e, then the largest possible value is a(m+e)+b= am+ ae+ b= (am+b)+ ae and the smallest possible is a(m-e)+ b= am-ae+ b= (am+b)- ae.

That is: (am+ b)+/- ae. Any added constants you can ignore. Constants multiplied by x multiply the error. Same for percentage error.

With more than one "uncertain" number you can get the exact error by calculating the maximum and minimum. A "rule of thumb" (good approximation but not exact) is that when you add or subtract measurements, the errors add, when you multiply or divide measurements, the percentage errors add.