SIG FIGURES RULE SUMMARY COUNTING S and Conversion

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SIG FIGURE’S RULE SUMMARY COUNTING #’S and Conversion factors – INFINITE n NONZERO DIGIT’S:

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

SIGNIFICANT FIGURE’S RULES FOR CALCULATIONS n CALCULATIONS USING MEASURED VALUES CAN BE NO MORE

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

Significant Figures Rules for Addition and Subtraction Add or subtract (i. e. , first

Significant Figures Rules for Addition and Subtraction Add or subtract (i. e. , first do the math) n Round to FEWEST PLACES past decimal n 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 n least accurate, 0 places past decimal)

Significant Figure Rules for Multiplication and Division n Multiply or Divide (i. e. ,

Significant Figure Rules for Multiplication and Division n 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 103 cm 3 (Rounded to least accurate, 2 SF)

Comparison of Significant Figure Rules for Calculations n n Addition & Subtraction Rule: Fewest

Comparison of Significant Figure Rules for Calculations n n Addition & Subtraction Rule: Fewest Places Past Decimal n Example: n n 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) n 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 103 cm 3 (Rounded to least accurate, 2 SF)

Significant Figures Problem Set HW 4 n 2 a) 3. 482 cm + 8.

Significant Figures Problem Set HW 4 n 2 a) 3. 482 cm + 8. 51 cm + 16. 324 cm n 2 a) ANS = 28. 316 → 28. 32 cm (2 places past decimal) 2 b) 48. 0032 g + 9. 17 g + 65. 4321 g = 2 b) ANS: 122. 6053 = 122. 61 g (2 places past decimal) 2 c) 80. 4 cm – 16. 532 cm = 2 c) ANS: 63. 868 → 63. 9 cm (1 place past decimal) 2 d) 106. 5 cm – 30. cm = 2 d) ANS: 76. 5 → 77 cm (1 place past decimal) n n n

Significant Figures Problem Set HW 4 n n n 2 e) 48. 2 cm

Significant Figures Problem Set HW 4 n n n 2 e) 48. 2 cm x 1. 6 cm x 2. 12 cm = 2 e) ANS: 163. 4944 cm 3 → 160 cm 3 (2 SF) 2 f) 64. 34 cm 3/ 8. 149 cm = 2 f) ANS: 7. 89544729 → 7. 895 cm 2 (4 SF) 2 g) 0. 057 m. L x (760 mm/ 740 mm) x (273 K/ 250 K) = 2 g) ANS: 0. 06392627 → 0. 064 m. L (2 SF)

Significant Figures Problem Set HW 43 a) 3. 0 x 108 m/s x 2

Significant Figures Problem Set HW 43 a) 3. 0 x 108 m/s x 2 x 106 s n 3 a) ANS: 6. 0 x 1014 m → 6 x 1014 m (1 SF) n 3 b) 1. 4 x 10 -2 m x 3. 25 x 10 -6 m n 3 b) ANS: 4. 55 x 10 -6 m 2 → 4. 6 x 10 -8 m 2 n 3 c) 6. 023 x 1014 mm 2 / 5. 81 x 1012 mm n 3 c) ANS: 1. 03666093 x 102 mm → n 1. 04 x 102 mm (3 SF) n