Simulation · Physics · Class 11
A power multiplies the error
From the lesson Uncertainty in calculated results in Units and Measurements. Change the values and watch what happens.
A power multiplies the errorPhysics · Class 11
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.