Rounding off

When a result carries more than one uncertain digit, round it to the right number of significant figures.

If the digit being dropped is more than 5, raise the preceding digit by 1 (2.746 → 2.75); if it is less than 5, leave the preceding digit alone (1.743 → 1.74).

If the digit being dropped is exactly 5, look at the preceding digit: if it is even, simply drop the 5 (2.745 → 2.74); if it is odd, raise it by 1 (2.735 → 2.74).

In a multi-step calculation, carry one digit more than the final answer needs through the intermediate steps and round only at the end, or rounding errors build up.

Rounding too early can shift an answer: 1/9.58 rounded to 0.104 and inverted gives 9.62, but keeping 0.1044 gives back 9.58.

Constants known to many figures are rounded to what the problem needs: c = 2.99792458 × 10⁸ m s⁻¹ is often used as 3 × 10⁸ m s⁻¹, and π as 3.14 or 3.142.

A cube of side 7.203 m has surface area 6 × (7.203)² = 311.3 m² and volume (7.203)³ = 373.7 m³, both to four significant figures; 5.74 g in 1.2 cm³ gives a density of 4.8 g cm⁻³, to two.