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).