1.1 Significant Figures

Significant figures and rounding.

Core idea

Significant figures communicate the precision of a measured or stated value.

  • Non-zero digits are significant.
  • Zeros between significant digits are significant.
  • Leading zeros are not significant.
  • Trailing zeros are significant when the notation makes the precision clear.
  • In scientific notation, the coefficient makes the intended significant figures clear.

Examples:

42.7 has 3 significant figures.
0.00420 has 3 significant figures.

Calculations

Adding and subtracting

Round the answer to the least precise decimal place.

16.3 + 17.14 = 33.44 → 33.4

Multiplying and dividing

Round the answer to the same number of significant figures as the value with the fewest significant figures.

6.23 × 1.23 = 7.6629 → 7.66 (3 significant figures)

Keep full calculator precision through the calculation and round once, at the end.

Class material

TipImprove these notes

Add one worked example or common mistake.