1. SIG FIGURE’S RULE SUMMARY
COUNTING #’S and Conversion factors – INFINITE
NONZERO DIGIT’S: ALWAYS
ZERO’S:
LEADING : NEVER
CAPTIVE: ALWAYS
TRAILING :SOMETIMES
Decimal present?
YES; SIGNIFICANT
NO; NOT SIGNIFICANT

2. SIGNIFICANT FIGURE’S RULES FOR CALCULATIONS
CALCULATIONS USING MEASURED VALUES CAN BE NO MORE ACCURATE THAN THE LEAST ACCURATE MEASUREMENT
POINT OF CONFUSION: Definition of “least accurate” is different from addition and subtraction compared to multiplication and division
Least accurate: Addition and Subtraction = Fewest places past decimal
Least accurate: Multiplication and Division = Fewest SF

3. Significant Figures Rules for Addition and Subtraction
Add or subtract (i.e., first do the math)
Round to FEWEST PLACES past decimal
Example: cm ← 2 places past decimal
cm ← 1 places past decimal
cm ← 0 places past decimal
→ 125 cm (Rounded to least accurate, 0 places past decimal)

4. Significant Figure Rules for Multiplication and Division
Multiply or Divide (i.e., first do math)
Round to final answer to same # of sig figures as factor with fewest SF
Example cm ← 3 SF
x cm ← 3 SF
cm ← 2 SF
→ 4.1 x 103 cm3
(Rounded to least accurate, 2 SF)

5. Comparison of Significant Figure Rules for Calculations
Addition & Subtraction
Rule: Fewest Places Past Decimal
Example:
3.05 cm ← 2 places past decimal
cm ← 1 places past decimal
cm ← 0 places past decimal
→ 125 cm (Rounded to least accurate, 0 places past decimal)
Multiplication and Division
Rule: Fewest SF
Example cm ← 3 SF
x cm ← 3 SF
cm ← 2 SF
→ 4.1 x 103 cm3
(Rounded to least accurate, 2 SF)

6. Significant Figures Problem Set HW 4-
2a) cm cm cm
2a) ANS = → cm (2 places past decimal)
2b) g g g =
2b) ANS: = g (2 places past decimal)
2c) 80.4 cm – cm =
2c) ANS: → 63.9 cm (1 place past decimal)
2d) cm – 30. cm =
2d) ANS: 76.5 → 77 cm (1 place past decimal)

7. Significant Figures Problem Set HW 4-
2e) 48.2 cm x 1.6 cm x 2.12 cm =
2e) ANS: cm3 → 160 cm3 (2 SF)
2f) cm3/ cm =
2f) ANS: → cm2 (4 SF)
2g) mL x (760 mm/ 740 mm) x (273 K/ 250 K) =
2g) ANS: → mL (2 SF)

8. Significant Figures Problem Set HW 4-
3a) 3.0 x 108 m/s x 2 x 106 s
3a) ANS: 6.0 x 1014 m → 6 x 1014 m (1 SF)
3b) 1.4 x10-2 m x 3.25 x 10-6 m
3b) ANS:4.55 x 10-8 m2 → 4.6 x 10-8 m2
3c) x 1014 mm2 / 5.81 x 1012 mm
3c) ANS: x 102 mm →
1.04 x 102 mm (3 SF)