1. METRIC AND MEASUREMENTS Scientific Notation Significant Digits Metric System Dimensional Analysis

2. SCIENTIFIC NOTATION Makes very large or small numbers easy to use Two parts: 1  x < 10 (including 1 but NOT 10) x 10 exponent

3. WRITING SCIENTIFIC NOTATION EXAMPLES: 1) 2,000,000,000 2) 5430 3) 0.000000123 6) 0.0000600 4) 0.007872 5) 966,666,000 = 2 X 10 9 = 5.43 X 10 3 = 1.23 X 10 -7 = 7.872 X 10 -3 = 6.00 X 10 -5 = 9.66666 X 10 8 LARGE NUMBERS (>1)POSITIVE EXPONENTS EQUAL TO 1 or itselfZERO EXPONENTS SMALL NUMBERS (<1)NEGATIVE EXPONENTS

4. WRITING STANDARD FORM EXAMPLES: 1) 4.32 X 10 7 2) 3.45278 X 10 3 3) 8.45 X 10 -5 6) 1.123 X 10 5 4) 5.0010 X 10 -9 5) 7.00 X 10 -1 = 43,200,000 = 3452.78 = 0.0000845 = 0.0000000050010 = 112,300 = 0.700 POSITIVE EXPONENTSMOVE TO RIGHT NEGATIVE EXPONENTS MOVE TO LEFT

5. SIGNIFICANT DIGITS Exact numbers are without uncertainty and error Measured numbers are measured using instruments and have some degree of uncertainty and error Degree of accuracy of measured quantity depends on the measuring instrument

6. RULES 1) All NONZERO digits are significant Examples: a) 543,454,545 b) 34,000,000 Examples: c) 65,945 2) Trailing zeros are NOT significant = 9 = 2 = 5 b) 234,500 = 1 a) 1,000 = 4 c) 34,288,900,000= 6

7. RULES CON’T 3) Zero’s surrounded by significant digits are significant Examples: a) 1,000,330,134 b) 534,001,000 Examples: c) 7,001,000,100 4) For scientific notations, all the digits in the first part are significant = 10 = 6 = 8 b) 2.34 x 10 -16 = 4a) 1.000 x 10 9 = 3 c) 3.4900 x 10 23 = 5

8. RULES CON’T 5) Zero’s are significant if a) there is a decimal present (anywhere) b) AND a significant digit in front of the zero Zero’s at beginning of a number are not significant (placement holder) Examples: a) 0.00100 b) 0.1001232 c) 1.00100 = 3 = 7 = 6 e) 0.0000007 = 9d) 8900.00000 = 1 f) 0.003400= 4 g) 0.0700= 3 = 5h) 0.040100

9. Rules for Rounding in Calculations

10. Rounding with 5’s: UP ____ 5 greater than zero 10.257= 10.3 34.3591 = 34.4  ODD 5 zero 99.750= 99.8 101.15 = 101.2

11. Rounding with 5’s: DOWN  EVEN 5 zero 6.850= 6.8 101.25 = 101.2

12. CALCULATIONS 1) Multiply and Divide: Least number of significant digits Examples: a) 0.102 x 0.0821 x 273 b) 0.1001232 x 0.14 x 6.022 x 10 12 c) 0.500 / 44.02 = 2.2861566 = 8.4412 x10 10 = 0.011358473 e) 150 / 4 = 2958.770205 d) 8900.00000 x 4.031 x 0.08206 0.995 = 37.5 f) 4.0 x 10 4 x 5.021 x 10 –3 x 7.34993 x 10 2 = 147615.9941 g) 3.00 x 10 6 / 4.00 x 10 -7 = 7.5 x 10 12

13. CALCULATIONS 2) Add and Subtract: Least precise decimal position Examples: a) 212.2 + 26.7 + 402.09 212.2 26.7 402.09 640.99 212.2 26.7 402.09 640.99 212.2 26.7 402.09 640.99 212.2 26.7 402.09 640.99 = 641.0

14. ADD AND SUBTRACT CON’T Examples: b) 1.0028 + 0.221 + 0.10337 1.0028 0.221 0.10337 1.32717 1.0028 0.221 0.10337 1.32717 1.0028 0.221 0.10337 1.32717 1.0028 0.221 0.10337 1.32717 = 1.327

15. ADD AND SUBTRACT CON’T Examples: c) 102.01 + 0.0023 + 0.15 102.01 0.0023 0.15 102.1623 102.01 0.0023 0.15 102.1623 102.01 0.0023 0.15 102.1623 102.01 0.0023 0.15 102.1623 = 102.16

16. ADD AND SUBTRACT CON’T Examples: d) 1.000 x 10 4 - 1 10000 - 1 9999 10000 - 1 9999 10000 - 1 9999 = 1.000 x 10 4

17. ADD AND SUBTRACT CON’T Examples: e) 55.0001 + 0.0002 + 0.104 55.0001 0.0002 0.104 55.1043 55.0001 0.0002 0.104 55.1043 55.0001 0.0002 0.104 55.1043 = 55.104

18. ADD AND SUBTRACT CON’T Examples: f) 1.02 x 10 3 + 1.02 x 10 2 + 1.02 x 10 1 1020 102 10.2 1132.2 1020 102 10.2 1132.2 1020 102 10.2 1132.2 1020 102 10.2 1132.2 = 1130

19. MIX PRACTICE Examples: a) 52.331 + 26.01 - 0.9981= 77.34= 77.3429 b) 2.0944 + 0.0003233 + 12.22 7.001 = 2.04466= 2.04 c) 1.42 x 10 2 + 1.021 x 10 3 3.1 x 10 -1 = 3751.613= 3.8 x 10 2 d) (6.1982 x 10 -4 ) 2 = 3.841768 x 10 -7 = 3.8418 x 10 -7 e) (2.3232 + 0.2034 - 0.16) x 4.0 x 10 3 = 9480= 9500

20. Why the Metric System? International unit of measurement: SI units Base units Derived units Based on units of 10’s

21. LENGTH Measure distances or dimensions in space Meter (m) Length traveled by light in a vacuum in 1/299792458 seconds.

22. MASS Measure of quantity of matter Kilogram (kg) Mass of a prototype platinum-iridium cylinder

23. TIME Forward flow of events Second (s) Time is the radiation frequency of the cesium-133 atom.

24. VOLUME Amount of space an object occupies Cubic meter (m 3 ) Derived unit 1 mL = 1 cm 3

25. METRIC PREFIXES PREFIXSYMBOLDEFINITION MEGA-M10 6 = 1,000,000 KILO-k10 3 = 1000 HECTO-h10 2 = 100 DECA-da10 1 = 10 BASE10 0 = 1 DECI-d10 -1 = 0.1 = 1/10 CENTI-c10 -2 = 0.01 = 1/100 MILLI-m10 -3 = 0.001 = 1/1000 MICRO-μ10 -6 = 0.000001 = 1/1,000,000 NANO-n 10 -9 = 0.000000001 = 1/1,000,000,000

26. DIMENSIONAL ANALYSIS Process to solve problems Factor-Label Method Dimensions of equation may be checked

27. DIMENSIONAL ANALYSIS Examples: a) 3 years = _______seconds 1 year = 365 days 1 day = 24 hours 1 hour = 60 minutes 1 min = 60 seconds 3 years 1 year 365 days 1 day 24 hours 1 hour 60 minutes 1 minute 60 seconds = 94608000 seconds= 9 x 10 7 seconds

28. DIMENSIONAL ANALYSIS Examples: b) 300.100 mL = ________kL 1 L = 1000 mL 1 kL = 1000 L 300.100 mL 1000 mL 1 L 1000 L 1 kL = 3.001 x 10 -4 kL= 3.00100 x 10 –4 kL

29. DIMENSIONAL ANALYSIS Examples: c) 9.450 x 10 9 Mg = _________dg 1 Mg = 10 6 g 1 g = 10 dg 9.450 x 10 9 Mg 1 Mg 10 6 g 1 g 10 dg = 9.450 x 10 16 dg

30. DIMENSIONAL ANALYSIS Examples: d) 2.356 g OH - = __________ molecules OH - 1 mole = 17 g OH - 1 mole = 6.022 x 10 23 molecules 2.356 g OH - 17 g OH - 1 mole OH - 6.022 x 10 23 molecules = 8.34578 x 10 22 molecules = 8.346 x 10 22 molecules

31. DIMENSIONAL ANALYSIS Examples: e) 45.00 km = __________cm 1 km = 1000 m 1 m = 100 cm 45.00 km 1 km 1000 m 1 m 100 cm = 4500000 cm = 4.500 x 10 6 cm

32. DIMENSIONAL ANALYSIS Examples: f) 6.7 x 10 99 seconds = _______years 1 year = 365 days 1 day = 24 hours 1 hour = 60 minutes 1 min = 60 seconds 6.7 x 10 99 seconds 60 seconds 1 minute 60 minutes 1 hours 24 hours 1 day 365 days 1 year = 2.124556 x 10 92 years= 2.1 x 10 92 years

33. DIMENSIONAL ANALYSIS Examples: g) 1.2400 g He = __________ Liters He 1 mole = 4 g He 1 mole = 22.4 L 1.2400 g He 4 g He 1 mole He 22.4 Liters He = 6.944 Liters He = 6.9440 Liters He