How to Solve R=(4.5±0.05)+(6.5±0.05)

Question

Please help me to solve this error calculations.

Answer 1

We need to find the minimum and maximum of R.

Minimum=4.5-0.05+6.5-0.05=4.45+6.45=10.90 (same as 4.5+6.5-0.10);

Maximum=4.55+6.55=11.10 (same as 4.5+6.5+0.10).

Therefore 10.90≤R≤11.10 or R=11.0±0.1.

You could also use the RMS of the two errors ε=√(0.05)²+(0.05)²)=0.05√2=0.07 approx., so R=11.00±0.07, which is the same as 10.93≤R≤11.07.