Which digits does the calculator really know?
"Which digits does the calculator really know?" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "Arithmetic with significant figures" in Units and Measurements. Two measured values drawn as uncertainty intervals; their sum/difference or product/quotient interval shows which digits of the calculator answer are actually known. NEET has asked about this idea 2 times in 10 years of papers. JEE Main asked 61 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Arithmetic with significant figures in Units and Measurements. Change the values and watch what happens.
What it shows
NCERT §1.3.1
Two measured values drawn as uncertainty intervals; their sum/difference or product/quotient interval shows which digits of the calculator answer are actually known.
Controls
4 to try
- Slidervalue 1 and its least count (0.1, 0.01, 0.001)
- Slidervalue 2 and its least count
- Toggleadd / subtract / multiply / divide
- Stepperdigits to report
Try this
Report 436.32 + 227.2 + 0.301 and 4.237 ÷ 2.51 with exactly the digits that lie inside the result's band (663.8 and 1.69).
Common mistake
Applying the fewest-significant-figures rule to sums, or the fewest-decimal-places rule to products.
In NEET
10 years of papers
Asked 2 times in 10 years of NEET.
See the past questions: Units and Dimensions, Units and Measurements (chapter)
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 §1.3.1
- A result calculated from measured values cannot be more precise than the data it came from, so it should not carry more significant figures than the data justify.
- Multiplication and division: keep as many significant figures as the input with the fewest significant figures. 4.237 g ÷ 2.51 cm³ gives 1.69 g cm⁻³, not 1.68804780876.
- Addition and subtraction: keep as many decimal places as the input with the fewest decimal places. 436.32 g + 227.2 g + 0.301 g = 663.821 g is reported as 663.8 g.
- Subtraction can cut the number of figures: the difference of 0.307 m and 0.304 m is just 3 × 10⁻³ m, one significant figure, although each input has three.
- Do not mix the two rules: the sum above is not 664 g, and the difference is not 3.00 × 10⁻³ m.
- With c = 3.00 × 10⁸ m s⁻¹ (three significant figures) and one year = 3.1557 × 10⁷ s (five), the light year comes out as 9.47 × 10¹⁵ m (three).
Questions
5 answers
- What does the "Which digits does the calculator really know?" simulation show?
- Two measured values drawn as uncertainty intervals; their sum/difference or product/quotient interval shows which digits of the calculator answer are actually known.
- What mistake does the "Which digits does the calculator really know?" simulation fix?
- A common mistake it clears up: applying the fewest-significant-figures rule to sums, or the fewest-decimal-places rule to products.
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 2 times in 10 years of papers.
- 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 "Arithmetic with significant figures" in Units and Measurements (Class 11 Physics).
Embed this simulation
Free, with a link back
Teaching this idea? Put the simulation on your own page or LMS with this code.