2. Significant Figures

3. SIGNIFICANT FIGURES You weigh something and the dial falls between 2.4 lb and 2.5 lb, so you estimate it to be 2.46 lb. The first two digits (2.4) are known. The last digit (6) is an estimate. All three digits convey useful information - are called significant figures

4. SIGNIFICANT FIGURES Includes all of the digits that are known plus a last digit that is estimated. The number of significant figures depends on the accuracy of the measuring device or instrument used to make the original measurements.

5. SIGNIFICANT FIGURES Read each measurement in “sig figs”: a.28 mL b.28.3 mL c.28.32 mL

6. SIGNIFICANT FIGURES Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the original measurements. You can’t say the measurement is 28.307594 mL for this beaker…

7. Exact v. Inexact Numbers Exact numbers –numbers known exactly (by definition or by counting) –One dozen = 12, one foot = 12 inches, 33 students in the room Inexact numbers – values with some uncertainty; anything measured using a piece of equipment (balance, graduated cylinder) –Mass of penny = 3.03 grams

8. Precision v. Accuracy Precision –how closely individual measurements agree (repeatability) Accuracy – how closely individual measurements agree with the correct or “true” value (bullseye) –Greater accuracy of an instrument means more significant figures.

9. Atlantic/Pacific rule If there is a decimal Present, count from the Pacific side If there is a decimal Absent (no decimal) count from the Atlantic side

10. Counting Sig Figs Atlantic/Pacific Rule PacificAtlantic

11. Decimal Present Count from the Pacific (left) side Start at the first non-zero number, count all numbers until the end of the number 0.0000565.0062010 45.201

12. Decimal Absent Count from the Atlantic (right) side Start at the first non-zero number and count all numbers until the start of the number 45210000 8900000 7254010000

13. SIGNIFICANT FIGURES RULE 1: Digits other than zero are always significant. Examples: 96 g 2 significant digits 61.4 g 3 significant digits 0.52 g 2 significant digits

14. SIGNIFICANT FIGURES RULE 2: Zeros between two other significant digits are always significant. Example: 5.029 m 4 significant digits 306 km 3 significant digits 6.02 x 10²³ particles 3 significant digits

15. SIGNIFICANT FIGURES RULE 3: For numbers less than 1: Start at first non-zero value and go to the end –Example: 7 0.007 g 1 significant digit 70 0.0070 g 2 significant digits 7830 0.007830 kg 4 significant digits

16. SIGNIFICANT FIGURES RULE 4: For numbers greater than 1: Start with the first digit and end with the last integer or decimal point. Example: 7 7000 g 1 significant digit 7000.0 7000.0 g 5 significant digits 7300 kg 2 significant digits

17. You Try! How many sig figs in the following: Examples: a) 1001 km b) 34.00 m c) 129,870 m d) 0.003 km e) 1.003 f) 0.0072561 g g) 20,000 cm h) 0.0023 g Number of Significant Figures: a) 4 b) 4 c) 5 d) 1 e) 4 f) 5 g) 1 h) 2

18. CALCULATIONS WITH SIG FIGS RULE: When multiplying or dividing measurements, round off the final answer to the number of significant figures in the measurement with the smallest number of significant figures.

19. CALCULATIONS WITH SIG FIGS Examples: 2.03 1. 2.03 cm x 36.00 cm = 73.08 cm² 73.1 = 73.1 cm² 1.13 2. (1.13 m)(5.126122m) = 5.7925178 m² 5.79 = 5.79 m² 47.40 3. 49.6000 cm² / 47.40 cm = 1.0464135 cm 1.046 = 1.046 cm

20. CALCULATIONS WITH SIG FIGS RULE: When adding or subtracting, round the answer to the same number of decimal places as the measurement with the smallest number of decimal places.

21. CALCULATIONS WITH SIG FIGS Examples: 145 1) 677.1 cm 2) 34.231 g 3) 16.45 cm 39.24 cm 6.709 g - 8.329 cm 20 + 6.232 cm + 18.20 g 8.121 cm 722.572 cm 59.140 g 6 = 722.6 cm 14 = 59.14 g 12 cm = 8.12 cm

22. You Try! Addition 165.5 cm + 8 cm + 4.37 cm = Multiplication 2.6 cm x 3.78 cm = 177.87 cm 178 cm = 178 cm 9.828 cm 2 9.8 cm 2 = 9.8 cm 2

23. Rounding Tips: When rounding number greater than or equal to 5: round up. Ex: 5.76 = 5.8 4.89 = 4.9 When rounding number less than 5: round down. Ex: 5.24 = 5.2 4.12 = 4.1