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)

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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 = a^pb^q / c^r
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.