Physics · Units And Measurements · NEET
No. This is the most common mistake. For Z = A - B, the maximum error is still ΔZ = ΔA + ΔB, the errors ADD. Reason: measurement errors can go either way (plus or minus). The worst case is when A is at its highest and B is at its lowest, or the reverse. In both worst cases the two errors pile up, they do not cancel. So we always add the absolute errors, whether the sign in the formula is plus or minus.
For sum and difference, you add ABSOLUTE errors (ΔA and ΔB), not percentage errors. This is the opposite of product and quotient, where you add percentage (relative) errors. Rule to remember: Sum/Difference -> add absolute errors. Product/Quotient -> add relative (percentage) errors. Mixing these two rules is a frequent NEET error.
When A and B are close, Z = A - B is a small number, but the absolute error ΔZ = ΔA + ΔB stays the same size. So the relative error ΔZ/Z becomes very large. Example: A = 5.02 cm, B = 5.00 cm, each with error 0.01 cm. Then Z = 0.02 cm but ΔZ = 0.02 cm, a 100% error. This is why physics experiments avoid measuring a small quantity as the difference of two large ones.
Write it as Z ± ΔZ, keeping ΔZ to one significant figure and rounding Z to the same decimal place. Example: if Z = 4.28 cm and ΔZ = 0.03 cm, write (4.28 ± 0.03) cm. The result and its error must end at the same decimal position.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
If Z = A + B or Z = A - B, the maximum absolute error is ΔZ = ΔA + ΔB. The absolute errors of the two quantities always add, regardless of the plus or minus sign in the formula.
Because an error can be positive or negative. To find the largest possible error, we take the worst case, where the errors of A and B combine in the same direction. That worst case gives ΔZ = ΔA + ΔB.
We add absolute errors. Percentage (relative) errors are added only for product and quotient, not for sum and difference.
No. The rule always adds the magnitudes of the errors, so ΔZ = ΔA + ΔB is never smaller than either error. Two equal errors give a larger total error, not zero.
For sum and difference you add absolute errors (ΔZ = ΔA + ΔB). For product and quotient you add relative errors (ΔZ/Z = ΔA/A + ΔB/B). Choosing the wrong rule is a common NEET slip.
