Simulation · Physics · Class 11

Percentage errors add when you multiply

From the lesson Uncertainty in calculated results in Units and Measurements. Change the values and watch what happens.

The idea behind it

NCERT §1.3.3

A reading from an instrument carries an uncertainty of about its least count: a length of 16.2 cm read on a metre scale is 16.2 ± 0.1 cm.
The relative (percentage) error is the uncertainty divided by the value: ±0.1 cm on 16.2 cm is about ±0.6%, and ±0.1 cm on 10.1 cm is about ±1%.
When measured values are multiplied or divided, their percentage errors add: the area l × b = 163.62 cm² carries ±1.6%, about ±2.6 cm², so it is quoted as 164 ± 3 cm².
The same absolute uncertainty is a larger relative error on a smaller value: ±0.01 g is ±1% of 1.02 g but only ±0.1% of 9.89 g.
Uncertainties in a sum or difference follow decimal places, not significant figures, so a difference can lose figures: 12.9 g − 7.06 g is 5.8 g, not 5.84 g.
If the data are good to n significant figures, a result obtained by combining them is valid to about n significant figures, fewer if data are subtracted.

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