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Significant Figures

Significant Figures. All non-zero digits are significant .    3971874351298   (13 sig. fig.) Zeros which start a number are never significant .  0.35 (2 sig. fig)   .0000587   (3 sig. fig) Zeros which are between other significant figures are significant .   2348762074003  (13 sf ).

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Significant Figures

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  1. Significant Figures • All non-zero digits are significant.    3971874351298   (13 sig. fig.) • Zeros which start a number are never significant.  0.35 (2 sig. fig)   .0000587   (3 sig. fig) • Zeros which are between other significant figures are significant.   2348762074003  (13 sf). • Zeros at the end of a number may be significant, if: • a decimal has been purposefully placed at the end of the number.    5000.   (4 sig. fig)     38000  (2 sig. fig.) • they follow other known significant figures and  the number starts with a decimal.      .0057200  (5 sig. fig.)

  2. Practice • How many significant figures are in each of the following number? 1.  368721                    2.  0.453                       3.  6704000                  4.  60                            5.  5700.                     

  3. Significant Figures, Scientific Notation, Unit Conversion, and Unit Magnitudes

  4. Practice • Change 2346.2005  to show 5 significant figures. • Change 6000 to 6 significant figures • Change 0.00085006 to 1 significant figure • Change 78.5 to 4 significant figures

  5. Rules for Calculations • Addition and Subtraction: • The number of decimal places in the answer should match the least number of decimal places in the problem • EX: 54.67 + 54.32 +54.0 + 54.777 + 54  = 271.767      The final answer here is 272 • Multiplication and Division • The number of significant figures in the answer should match the least number of significant figures in the problem • EX: 3.0 X 395.2 X 0.002 = 2.3712 The final answer is 2

  6. Rules for Calculations • Exact Numbers do not limit the # of sig figs in the answer. • Counting numbers: 12 students • Exact conversions: 1 m = 100 cm • “1” in any conversion: 1 in = 2.54 cm

  7. Practice • 7846 X 92437  X 235.649 X 3300 • ANS: 560000000000000 • 583.00÷83 • ANS: 7.0 • 567.000 – 12 • ANS: 555 • 78.00 + 45.6 + 0.00467 + 39.45 + 276.999 • ANS: 440.0 • (350000)  X [2.8 ÷ (5.4  - 4.09)] • ANS: 750000

  8. Scientific Notation • Scientific notation is simply a method for expressing, and working with, very large or very small numbers.  • -Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent. • -EX: 5.67 x103 is the scientific notation for 5670 -5.67 x 105 coefficientbaseexponent

  9. Scientific Notation 1. The coefficient must be greater than or equal to 1 and less than 10. 2. The base must be 10. 3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation.  A negative exponent means that the decimal is moved to the left when changing to standard notation.

  10. Converting to Scientific Notation • Move decimal until there’s 1 digit to its left. • -Places moved = exponent. • Large # (>1)  positive exponent • Small # (<1)  negative exponent • EX: Put 987000000000000000 in scientific notation • 9.87 x1017 • Practice

  11. EXE EXP EXP ENTER EE EE Scientific Notation • Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: 5.44 7 8.1 4 ÷ = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

  12. Unit Conversion • SI units: The International System of Units (abbreviated SI from the French Systèmeinternational d'unités]) is the modern form of the metric system • a system of units of measurement devised around seven base units and the convenience of the number ten

  13. Unit Conversion • I will give you there conversion factors if you need them in a problem! • 1 inch = 2.54 cm • exactly 1 lb = 454 g • 1 qt = 0.946 L • 1 mi = 5280 ft • 1 qt = 2 pt • 4qt = 1 gal • 1 ounce = 28.349523 grams

  14. Unit Conversions • Convert 3598 grams into pounds. (exactly 1 lb = 454 g ) ANS: 7.925 lbs

  15. Unit Conversions • Convert 231 grams into ounces. (1 ounce = 28.349523 grams) ANS:8.15 ounces

  16. Unit Conversions • How many gallons are in 5.67 L? (1 qt = 0.946 L and 4qt = 1 gal) ANS: 1.50

  17. Unit Magnitudes

  18. Dimensional Analysis • Dimensional Analysis • A tool often used in science for converting units within a measurement system • Conversion Factor • A numerical factor by which a quantity expressed in one system of units may be converted to another system

  19. Dimensional Analysis • The “Factor-Label” Method • Units, or “labels” are canceled, or “factored” out

  20. Dimensional Analysis • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

  21. Dimensional Analysis Practice How many seconds are in 1.4 days? Plan: days hr min seconds 1.4 days x 24 hr x 60 min x 60 sec = 1 day 1 hr 1 min 120960 sec 120000 sec

  22. Classwork/Homework • Start reading chapter 1 • You will need information covered in this chapter to complete the lab on Thursday!

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