Let y = l2 - l3/z where l = 2.0 \( \pm 0.1\) , z= 1.0\( \pm 0.1\) then the value of y is given by
a) 2 \( \pm 0.8\)
b) -4 \( \pm 1.6\)
c) -4 \( \pm 0.8\)
d) none of these.
Answer is given as b). Kindly explain.
Error looks bit high especially in z (10%). Let's go by the basic approach:
| I | z | y |
| 2.1 | 1.1 | -4.0 |
| 2.1 | 0.9 | -5.9 |
| 1.9 | 1.1 | -2.6 |
| 1.9 | 0.9 | -4.0 |
ymean=2.02-2.03/1.0=-4.0
Since we are interested in maximum error, we look at -5.9 and -2.6.
|Δy1| = |-4.0+5.9|=1.9
|Δy2| = |-4.0+2.6|=1.4
Δymean = Average of 1.9 and 1.4 = 1.6
Answer = ymean ± Δymean