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METRIC AND MEASUREMENTS

METRIC AND MEASUREMENTS. Scientific Notation Significant Digits Metric System Dimensional Analysis. SCIENTIFIC NOTATION. Makes very large or small numbers easy to use Two parts:. 1  x < 10 (including 1 but NOT 10). x 10 exponent. WRITING SCIENTIFIC NOTATION. EXAMPLES:.

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METRIC AND MEASUREMENTS

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

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

  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 = 9 b) 34,000,000 = 2 = 5 c) 65,945 2) Trailing zeros are NOT significant Examples: = 1 a) 1,000 b) 234,500 = 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 = 10 b) 534,001,000 = 6 c) 7,001,000,100 = 8 4) For scientific notations, all the digits in the first part are significant Examples: a) 1.000 x 10 9 = 4 b) 2.34 x 10 -16 = 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 = 3 e) 0.0000007 = 1 f) 0.003400 = 4 b) 0.1001232 = 7 c) 1.00100 = 6 g) 0.0700 = 3 d) 8900.00000 = 9 h) 0.040100 = 5

  9. Rules for Rounding in Calculations

  10. Rounding with 5’s: • UP • ____ 5 greater than zero 10.257 = 10.3 34.3591 = 34.4 • ODD5 zero 99.750 = 99.8 101.15 = 101.2

  11. Rounding with 5’s: • DOWN • EVEN5 zero 6.850 = 6.8 = 101.2 101.25

  12. CALCULATIONS • Multiply and Divide: Least number of significant digits Examples: a) 0.102 x 0.0821 x 273 = 2.2861566 b) 0.1001232 x 0.14 x 6.022 x 10 12 = 8.4412 x1010 c) 0.500 / 44.02 = 0.011358473 d) 8900.00000 x 4.031 x 0.08206 0.995 = 2958.770205 = 37.5 e) 150 / 4 f) 4.0 x 104 x 5.021 x 10–3 x 7.34993 x 102 = 147615.9941 g) 3.00 x 10 6 / 4.00 x 10 -7 = 7.5 x 1012

  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 104 - 1 10000 - 1 9999 10000 - 1 9999 10000 - 1 9999 = 1.000 x 104

  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 103 + 1.02 x 102 + 1.02 x 101 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 = 77.3429 = 77.34 b) 2.0944 + 0.0003233 + 12.22 7.001 = 2.04466 = 2.04 c) 1.42 x 102 + 1.021 x 103 3.1 x 10 -1 = 3751.613 = 3.8 x 102 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 103 = 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 (m3) • Derived unit • 1 mL = 1 cm3

  25. METRIC PREFIXES

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

  27. DIMENSIONAL ANALYSIS Examples: • 3 years = _______seconds 1 year = 365 days 1 day = 24 hours 1 hour = 60 minutes 1 min = 60 seconds 3 years 365 days 24 hours 60 minutes 60 seconds 1 year 1 day 1 hour 1 minute = 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 1 L 1 kL 1000 mL 1000 L = 3.001 x 10-4 kL = 3.00100 x 10 –4 kL

  29. DIMENSIONAL ANALYSIS Examples: c) 9.450 x 109 Mg = _________dg 1 Mg = 10 6 g 1 g = 10 dg 9.450 x 109 Mg 10 6 g 10 dg 1 Mg 1 g = 9.450 x 1016 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 - 1 mole OH - 6.022 x 1023 molecules 17 g OH - 1 mole OH - = 8.34578 x 1022 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 1000 m 100 cm 1 km 1 m = 4500000 cm = 4.500 x 10 6 cm

  32. DIMENSIONAL ANALYSIS Examples: f) 6.7 x 1099 seconds = _______years 1 year = 365 days 1 day = 24 hours 1 hour = 60 minutes 1 min = 60 seconds 6.7 x 1099 seconds 1 hours 1 minute 1 day 1 year 60 seconds 60 minutes 24 hours 365 days = 2.124556 x 1092 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 1 mole He 22.4 Liters He 4 g He 1 mole He = 6.944 Liters He = 6.9440 Liters He

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