Percentage errors add when you multiply
"Percentage errors add when you multiply" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the lesson "Uncertainty in calculated results" in Units and Measurements. Pick the instrument for each side. A metre scale reads to 0.1 cm, vernier callipers to 0.01 cm. Watch the area, its significant figures and its uncertainty. In a product or quotient, percentage errors add and the answer keeps the fewest significant figures of the inputs. The same absolute error hurts a small value more. JEE Main asked 61 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Uncertainty in calculated results in Units and Measurements. Change the values and watch what happens.
In JEE Main
42 shifts analysed
61 questions from Units and Measurements across the 42 JEE Main shifts Lumi has analysed (2017–2026).
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.
Questions
3 answers
- What does the "Percentage errors add when you multiply" simulation show?
- Pick the instrument for each side. A metre scale reads to 0.1 cm, vernier callipers to 0.01 cm. Watch the area, its significant figures and its uncertainty.
- Does JEE Main ask questions from Units and Measurements?
- Yes. JEE Main asked 61 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Uncertainty in calculated results" in Units and Measurements (Class 11 Physics).
Embed this simulation
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