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Chapter 3 lec 2: Significant Figures

Chapter 3 lec 2: Significant Figures. What is the difference between the values of 3, 3.0, and 3.00. Significant Figures. Important digits in a value. Not all digits in a measurement are considered significant figures. There are rules for determining the number of significant figures.

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Chapter 3 lec 2: Significant Figures

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  1. Chapter 3 lec 2: Significant Figures • What is the difference between the values of 3, 3.0, and 3.00

  2. Significant Figures • Important digits in a value. • Not all digits in a measurement are considered significant figures. • There are rules for determining the number of significant figures.

  3. Rules for Significant Figures 1. Non-zero numbers are always significant. Ex. 72.3 has 3 significant figures.

  4. Rules for Significant Figures 1. Non-zero numbers are always significant. Ex. 72.3 has 3 significant figures. 2. Zeros between non-zero numbers are always significant. Ex. 60.5  has 3 significant figures.

  5. Rules for Significant Figures 1. Non-zero numbers are always significant. Ex. 72.3 has 3 significant figures. 2. Zeros between non-zero numbers are always significant. Ex. 60.5  has 3 significant figures. 3.Zeros before (to the left of) non-zero numbers are not significant. Ex. 0.0253  has 3 significant figures

  6. 4. All Zeros after (to the right of) non-zero numbers are significant IF there is a decimal point in the number. Ex. 123.00  5 significant figures (decimal) Ex. 12,000  2 significant figures (no decimal) Ex. 120.0  4 significant figures (decimal) Ex. 12,000.  5 significant figures (decimal)

  7. Atlantic Pacific rule https://www.youtube.com/watch?v=HB1l5-ePNWw

  8. Let’s try some together…. How many significant digits are in these numbers? • 35 g • 3.57 m • 3.507 km • 0.0035 kg • 2406 L • .0004 m • 240.00 g • 20.04080 g

  9. How did you do? • 35g 2 • 3.57m 3 • 3.507km 4 • 0.0035kg 2 • 2406 L 4 • .0004m 1 • 240.00 g 5 • 20.04080 g 7

  10. Rounding Numbers • Often times your calculator will give you more digits than necessary. In these cases you will round. Let try a few. 1. Round 3.515014 to 5 significant figures. = 3.5150 2. Round 3.5150 to 3 significant figures = 3.52 3. Round 3.52 to 1 significant figure = 4 4. Round 3430 to 2 significant figures = 3400

  11. Round all of the numbers to four significant figures a. 84791 kg b. 38.5432 g c. 256.75 cm d. 4.9356 m e. 0.00054818 g f. 136,758 kg g. 308,659,000 mm h. 2.0142 ml

  12. Round all of the numbers to four significant figures a. 84791 kg = 84790 kg b. 38.5432 g = 38.54 g c. 256.75 cm = 256.8 cm d. 4.9356 m = 4.936 m e. 0.00054818 g = 0.00005482 g or 5.482 x 10-5g f. 136,758 kg = 136,800 kg or 1.368 x 105 kg g. 308,659,000 mm = 308,700,000mm or 3.087 x 108mm h. 2.0142 ml = 2.014 ml

  13. Calculations with significant figures 1. For addition and subtraction, the answers should be rounded off to the same number of decimal points as the measurement with the fewest decimal places. Ex. 2.56 + 2.1 = 4.66  4.7 Ex. 34.232 + 22.4 = 56.632  56.6 2. For multiplication and division, the answers should be rounded off to the same number of significant figures in the measurement with the fewest significant figures Ex. 3.01 x 2.0 = 6.02  6.0 Ex. 45 / 9.00 = 5.00  5.0

  14. Practice: • 4.5 + 2.34 = _____________________ 2) 6.00 + 3.411 = _____________________ 3) 3.4 x 2.32 = _______________________ 4) 7.77 / 2.3 = ______________________ 5) 3.890 / 121 = ______________________

  15. 6) 1200 x 23.4 = ______________________ 7) 120 x 0.0002 = _____________________ 8) 78.5 + 0.0021 + 0.0099 = ___________ 9) (3.4 x 8.90) x (2.3 + 9.002) = _________ 10) (2.31 x 103) / (3.1 x 102) = ___________ 11) 0.0023 + 65 = __________________

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