Lesson 4 of 10 · 8 min
Arithmetic with significant figures
NCERT §1.3.1
Riya's calculator shows g = 9.8103868 m s⁻². Her thread was known to three figures. How many of those eight digits has she really earned?
The lesson in notes
In short
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).