Estimate the error?

Question

Two lengths X and Y are measured approximately up to three significant figures as X=3.32 cm and Y=5.39 cm. Estimate the error in the computed value of X+Y.

Answer 1

Three significant figures means that the fourth figure was rounded. A standard estimate for the rounding error is ±1/2 of the least significant figure. In this case, both X and Y would have an error of ±0.005 cm.

 

Addition is also roughly estimated to add the errors of the the addends. Therefore, X+Y would have an error of ±0.01 cm.

 

There are many ways to estimate the error. This is the most conservative.