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

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

2. 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.)

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

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. 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

6. 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.

7. 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

8. 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

9. 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

10. Unit Conversion • I will give you these 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

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

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

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

14. Unit Magnitudes

15. 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

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

17. 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.

18. 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

19. Classwork/Homework • If you feel like you need more practice with these concepts you should….. • Read Chapter 1 • Pgs 24-27 • Numbers: 38, 45, 50,55, 60,67,71,72