Simulation · Physics · Class 11
Which digits does the calculator really know?
From the lesson Arithmetic with significant figures in Units and Measurements. Change the values and watch what happens.
Which digits does the calculator really know?Physics · Class 11
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).