Combination of Errors – Units and Measurement

Combination of Errors
(i) Error in Addition or Subtraction :
Let x = a + b or x = a- b
If the measured values of two quantities a and b are (a ± Δa) and (b ± Δb), then maximum absolute error in their addition or subtraction is

Δx = ± (Δa + Δb)

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

Combination of Error Formula, Definition, Rules

(ii) Combination of Errors in Multiplication or Combination of Errors in Division:
Let x = a x b or x = \(\frac{a}{b}\)
If the measured values of a and b are (a ± Δa) and (b ± Δb), then maximum relative error

\(\left(\frac{\Delta a}{a}+\frac{\Delta b}{b}\right)\)

(iii) Error in case of a measured quantity raised to a Power:
Let z = apbq / cr
If the measured values of a, b and c are (a ± Δa), (b ± Δb) and (c ± Δc), then maximum error

\(\frac{\Delta z}{z}=p\left(\frac{\Delta a}{a}\right)+q\left(\frac{\Delta b}{b}\right)+r\left(\frac{\Delta c}{c}\right)\)

Note: The smallest value that can be measured by a measuring instrument is called least count of that instrument, eg. A metre scale having graduation at 1 mm division scale spacing, has a least count of 1 mm or 0.1 cm.

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors