Answer to Question #258308 in Physics for jay

Question

Two lengths are recorded as (1.873 ± 0.005) mm and (1.580 ± 0.005) mm. What is the maximum

possible value of the sum of the two lengths and what is the maximum possible value of the difference

between the two lengths? What is the fractional uncertainty in both the sum of the two lengths and the

difference between the two lengths?

Answer 1

The maximum possible value of the sum:

$$L_1=1.873+0.005+1.580+0.005=3.463\text{ mm}.$$

The maximum possible value of the difference between the two lengths:

$$L_2=1.873+0.005-(1.580-0.005)=0.303\text{ mm}.$$

The fractional uncertainty in both the sum of the two lengths and the difference between the two lengths:

$$\epsilon_1=\frac{0.005+0.005}{L_1}·100\%=29\%,\\\space\\ \epsilon_2=\frac{0.005+0.005}{L_2}·100\%=3.3\%.$$