Significant Figures Rules: Multiplication/Division and Addition/Subtraction

Multiplication and Division: Significant Figures

• For multiplication and division, the answer's significant figures should equal the least significant figures among the numbers given.
• Formal rule: Let s(x) denote the number of significant figures in x. Then s(a \times b) = \min\left( s(a),\; s(b) \right).
• Example: 2.5 (2 sig figs) \times 3.95 (3 sig figs) = 9.875. Round to 2 sig figs: 9.9.

Addition and Subtraction: Significant Figures

• For addition and subtraction, the answer's decimal places should equal the least decimal places among the inputs.
• Formal rule: Let d(x) denote the number of digits to the right of the decimal point in x. Then d(a + b) = \min\left( d(a),\; d(b) \right).
• Example: 2.5 (1 decimal place) + 3.95 (2 decimal places) = 6.45. Round to 1 decimal place: 6.4.
• Rounding rules for the final value (to the specified decimal place):
  • If the discarded digit is greater than 5, round up.
  • If it is less than 5, round down.
  • If it is exactly 5, use round half to even (banker's rounding): round up if the preceding digit is odd, round down if even.
  • Examples for tie-to-even: 6.45 \to 6.4 (preceding digit 4 is even), 6.55 \to 6.6 (preceding digit 5 is odd).