Calculate the quantity and its error?

Question

The measured values are d1=3.42+-.01m, d2=7.65+-.05m. d=d2-d1. Calculate d and its error.

Answer 1

d1 = 3.42 + 0.01m

d2 = 7.65 - 0.05m

d = d2 - d1

d = (7.65 - 0.05m) - (3.42 + 0.01m)

d = 7.65 - 0.05m - 3.42 - 0.01m

d = 7.65 - 3.42 - 0.05m - 0.01m

d = 4.23 - 0.04m

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

No error.

Answer 2

d2-d1 should be done in any ordinary way. Thus, 7.65-3.42=4.23. But when dealing with errors, you should do the following.

In the first place, errors are always added.

when quantities are added or subtracted, errors are always added in relative form.(the form you have given)

when quantities are multiplied or divided, errors should be added in percentage form. eg. 0.01/3.42 x 100= +-0.292%

In your case, errors are added, thus, 0.01+0.05=0.06.

Your final answer is 4.23+-0.06