Question

Problem 1 (About uncertainty in addition and subtraction) You are trying to measure the height of a table using a 30-cm ruler. Since the ruler is not long enough, you do the measurement on 3 steps and you obtain the following results di = 30.0 +0.1 cm dz = 30.0 + 0.1 cm dz = 16.6 + 0.1 cm What is the total height of the table, di + d2 + dz?

Answer 1

for addition operation like asked above

d₁+d₂+d₃ = (30+30+16.6) $\pm$ (0.1+0.1+0.1) cm

d₁+d₂+d₃ = 76.6 $\pm$ 0.3 cm. ANS

other example:

in case of substraction

d₁-d₂+d₃ = (30-30+16.6) $\pm$ (0.1+0.1+0.1) cm

d₁-d₂+d₃ = 16.6  $\pm$ 0.3 cm

note: tolerances will add always add up irrespective of addition or subtraction.