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: 3.05 cm ← 2 places past decimal + 12.1 cm ← 1 places past decimal 110 cm ← 0 places past decimal 125.15 → 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 3.05 cm ← 3 SF x 12.1 cm ← 3 SF 110 cm ← 2 SF 4059.55 → 4.1 x 10 3 cm 3 (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 + 12.1 cm ← 1 places past decimal 110 cm ← 0 places past decimal 125.15 → 125 cm (Rounded to least accurate, 0 places past decimal) Multiplication and Division Rule: Fewest SF Example 3.05 cm ← 3 SF x 12.1 cm ← 3 SF 110 cm ← 2 SF 4059.55 → 4.1 x 10 3 cm 3 (Rounded to least accurate, 2 SF)

6. Significant Figures Problem Set HW 4- 2a) 3.482 cm + 8.51 cm + 16.324 cm 2a) ANS = 28.316 → 28.32 cm (2 places past decimal) 2b) 48.0032 g + 9.17 g + 65.4321 g = 2b) ANS: 122.6053 = 122.61 g (2 places past decimal) 2c) 80.4 cm – 16.532 cm = 2c) ANS: 63.868 → 63.9 cm (1 place past decimal) 2d) 106.5 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: 163.4944 cm 3 → 160 cm 3 (2 SF) 2f) 64.34 cm 3 / 8.149 cm = 2f) ANS: 7.89544729 → 7.895 cm 2 (4 SF) 2g) 0.057 mL x (760 mm/ 740 mm) x (273 K/ 250 K) = 2g) ANS: 0.06392627 → 0.064 mL (2 SF)

8. Significant Figures Problem Set HW 4- 3a) 3.0 x 10 8 m/s x 2 x 10 6 s 3a) ANS: 6.0 x 10 14 m → 6 x 10 14 m (1 SF) 3b) 1.4 x10 -2 m x 3.25 x 10 -6 m 3b) ANS:4.55 x 10 -6 m 2 → 4.6 x 10 -8 m 2 3c) 6.023 x 10 14 mm 2 / 5.81 x 10 12 mm 3c) ANS: 1.03666093 x 10 2 mm → 1.04 x 10 2 mm (3 SF)