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MEASUREMENT # 1

MEASUREMENT # 1. Metric System Unit Conversions Multiple Conversions. A measurement must include some form of unit (otherwise its just a number) E.g. 10.5 cm 247.93 g 0.25 mL. Base Units. Basic unit of measurement

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MEASUREMENT # 1

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  1. MEASUREMENT # 1 Metric System Unit Conversions Multiple Conversions Spectrum Community School Chemistry 11

  2. A measurement must include some form of unit (otherwise its just a number) • E.g. • 10.5 cm • 247.93 g • 0.25 mL Spectrum Community School Chemistry 11

  3. Base Units • Basic unit of measurement • Other units are multiples of base unit or combination of base units Spectrum Community School Chemistry 11

  4. Common Multiples of Base Units See table in text p. 18 for more complete list Spectrum Community School Chemistry 11

  5. Derived Units(two or more base units combined) Spectrum Community School Chemistry 11

  6. Unit Conversions • Used extensively in Chem 11 to relate quantities, find equivalent amounts and solve problems • Write initial amount (with units) then choose correct conversion factor Spectrum Community School Chemistry 11

  7. Conversion Factors • A fractional expression relating or connecting two different units. • E.g. 1 minute = 60 seconds • Conversion factor is • 1 min or60 s 60 s 1 min • Note these are both ratios equivalent to 1 Spectrum Community School Chemistry 11

  8. Example # 1 • 180 s = ? min • Choose conversion factor to multiply so that units will cancel • Unknown = initial amount X conversion amount factor • ??? min = 180 s X 1 min 60 s Spectrum Community School Chemistry 11

  9. ??? min = 180 s X 1 min 60 s • Cross out matching units (must be top and bottom) • Multiply or divide as indicated Spectrum Community School Chemistry 11

  10. ??? Min = 180 s X 1 min = 180 min 60 s 60 • Divide • Answer = 3 min Spectrum Community School Chemistry 11

  11. Example # 2 • 3.52 m = ? cm • Conversion factor: 1 m = 100 cm • Unknown = 3.52 m X 100 cm amount 1 m Spectrum Community School Chemistry 11

  12. Example # 2 • Unknown = 3.52 m X 100 cm amount 1 m • Cancel units then multiply • Answer = 352 cm Spectrum Community School Chemistry 11

  13. Note: • When units are included, the correct conversion factor is apparent and the correct multiplier (or divisor) is clear. Spectrum Community School Chemistry 11

  14. Practice - Convert the following(on separate page/show all work) • 1) 5 s into milliseconds • 2) 34 cL into litres • 3) 3 L into microlitres • 4) 45 hg into grams • 5) 7 Mm into metres Spectrum Community School Chemistry 11

  15. Multiple Conversions • Two or more conversion factors can be used in the same problem • Be consistent with units in all steps. Units will cancel if conversion factors chosen correctly. Spectrum Community School Chemistry 11

  16. Example # 3 • Convert 0.25 kL into mL • Can use 2 conversion factors • 1 kL = 1000 L • 1000000 mL = 1 L Spectrum Community School Chemistry 11

  17. Example # 3 • Convert 0.25 kL into mL • Unknown amt = initial amt x conv factors ___ mL = 0.25 kL x 1000 L x 1000000 mL • 1 kL 1 L ___ mL = 0.25 x 1000 x 1000000 mL = 250,000,000mL = 2.5 x 108mL Spectrum Community School Chemistry 11

  18. Relating Different Quantities • Any statement that relates different quantities can be a conversion factor • E.g. Gas costs 118.9 cents per litre • A case of Pepsi has 12 cans • The speed of a car is 75 km per hour Spectrum Community School Chemistry 11

  19. Example # 4The speed of a car is 75 km per hour • How far does this car go in 3 hours? • Unknown = 3 hrs X 75 km amount 1 hr Distance = 225 km Spectrum Community School Chemistry 11

  20. Example # 5 • The gas price in Seattle Washington is $2.49 US dollars per US gallon. • How much is this in Canadian dollars per litre? • Need 2 conversion factors: • 1 US gallon = 3.79 L • $1.00 US = $1.29 Canadian Spectrum Community School Chemistry 11

  21. Example # 5 • Unknown = Initial X 1st Conv X 2nd Conv amount amount factor factor • $ (Can) = $ 2.49 (USD) X 1 US gal X $1.29 Can 1 US gal 3.79 L $1.00(USD) • Cancel pairs of matching units (top & bottom) Spectrum Community School Chemistry 11

  22. Example # 5 • $ (Can) = $ 2.49 (USD) X 1 US gal X $ 1.29 Can 1 US gal 3.79 L $1.00(USD) • $ (Can) = 2.49 X $ 1.29 Can 3.79 L • $ (Can) = $0.8475per litre = 84.8 cents/L Spectrum Community School Chemistry 11

  23. Practice - Convert the following(add to previous/show all work) • 6) 2.8 mg into centigrams • 7) 1234 mL into hectolitres • 8) 36 kg into decigrams • 9) 1 g/mL into kg/L • 10) 1 year into seconds Spectrum Community School Chemistry 11

  24. Measurement Part 2 Scientific Notation Significant Figures Chemistry 11 - Spectrum Community School

  25. Scientific Notation(also called Exponential Notation) • A shorthand method of displaying very large or very small numbers. • Consists of a coefficient (or mantissa) and a power of 10 • E.g. 3.95 x 10 -2 • coefficient between 1 and 10 • Positive exponent - number is > 1 • Negative exponent - number is < 1 Chemistry 11 - Spectrum Community School

  26. Express in Scientific Notation • E.g. 3756 = ? • 3756 = 3.756 x 103 • 0.000493 = ? • 0.000493 = 4.93 x 10 -4 Chemistry 11 - Spectrum Community School

  27. Express in Standard Notation(Decimal Notation) • E.g. 5.21 x 104 = • 5.21 x 104 = 52100 • 2.694 x 10-5 • 2.694 x 10-5 = 0.00002694 Chemistry 11 - Spectrum Community School

  28. Practice • 1. 8720000 = • 2. 0.0000513 = • 3. 5302 = • 4. 0.00117 = • 5. 7.03 x 10-2 = • 6. 1.38 x 104 = • 7. 3.99 x 10-5 = • 8. 2.781 x 107 = Chemistry 11 - Spectrum Community School

  29. Answers 8.72 x 106 5.13 x 10-5 5.302 x 103 1.17 x 10-3 0.0703 13800 0.0000399 27810000 • 1. 8720000 = • 2. 0.0000513 = • 3. 5302 = • 4. 0.00117 = • 5. 7.03 x 10-2 = • 6. 1.38 x 104 = • 7. 3.99 x 10-5 = • 8. 2.781 x 107 = Chemistry 11 - Spectrum Community School

  30. 100 times bigger 100 times smaller Note: Coefficient must be between 1 and 10 • E.g. 73.59 x 103 • 73.59 is greater than 10 • Change to 7.359 (smaller by power of 10) and 104 (bigger by a power of 10) • = 7.359 x 104 • E.g. 0.0369 x 10-3 • = 3.69 x 10-5 Chemistry 11 - Spectrum Community School

  31. Write as Correct Scientific Notation • 1. 34.79 x 103 = • 2. 0.497 x 106 = • 3. 19.5 x 10-2 = • 4. 0.837 x 10-4 = Chemistry 11 - Spectrum Community School

  32. Write as Correct Scientific Notation - Answers 3.479 x 104 4.97 x 105 1.95 x 10-1 8.37 x 10-5 • 1. 34.79 x 103 = • 2. 0.497 x 106 = • 3. 19.5 x 10-2 = • 4. 0.837 x 10-4 = Chemistry 11 - Spectrum Community School

  33. Homework • Do Exponential Notation Worksheet • (1/2 page) Chemistry 11 - Spectrum Community School

  34. Significant Figures • When counting objects we can usually find an exact number • eg numbers of students in class • When measuring quantities there is usually some amount of uncertainty in the number • eg length of classroom • We need to have an idea of which digits are meaningful and which are not Chemistry 11 - Spectrum Community School

  35. A student measures the length of the classroom and reports it as 5.61875 m • How many of these digits are meaningful? • It depends on the tool used to measure. Chemistry 11 - Spectrum Community School

  36. Significant Figures • A significant figure (or significant digit) is a measured or meaningful digit. • Significant figures (or “Sig fig’s”) are the digits known to be precise (exact) plus one more that may have some uncertainty • The following examples show how many digits can be determined in different cases. Chemistry 11 - Spectrum Community School

  37. Rules for Significant Figures • A) all non zero digits are significant • B) zero’s are significant if: • They are at the end of a number if decimal point is shown • They are enclosed by non-zero numbers • C) zeros that hold place value only are not significant Chemistry 11 - Spectrum Community School

  38. Examples • 34.500 • 5 significant figures • 0.0087 • 2 significant figures • 3507 • 4 significant figures Chemistry 11 - Spectrum Community School

  39. Trailing Zeros Exception • 61000 2 sig figs (zeros are not significant) • If more sig figs are intended write in Scientific Notation Chemistry 11 - Spectrum Community School

  40. Same number Different Sig. Figs. • 1200 • 1200.0 • (Note 1200. is not legal usage - if decimal is written a digit must follow it) • 1.2 x 103 • 1.20 x 103 Chemistry 11 - Spectrum Community School

  41. Same number Different Sig. Figs. • 1200 2 sig figs (zeros not significant) • 1200.0 5 sig figs • (Note 1200. is not legal usage - if decimal is written a digit must follow it) • 1.2 x 103 2 sig figs • 1.20 x 103 3 sig figs Chemistry 11 - Spectrum Community School

  42. Perfect Numbers • Counting numbers or defined values are considered to be exact or perfect numbers and are exempt from rules of sig. figs. Chemistry 11 - Spectrum Community School

  43. Practice - How many Sig Figs • 13.0 mm • 48.07 g • 0.05 cm • 1001 L • 5 students • 15000 g • 1 L = 1000 mL • 3.00 x 10 -3 m Chemistry 11 - Spectrum Community School

  44. Practice - How many Sig Figs 3 sig figs 4 sig figs 1 sig fig 4 sig figs Perfect number 2 sig figs Perfect number 3 sig figs • 13.0 mm • 48.07 g • 0.05 cm • 1001 L • 5 students • 15000 g • 1 L = 1000 mL • 3.00 x 10 –3 m Chemistry 11 - Spectrum Community School

  45. On the centimetre ruler above we know the length at the arrow is between 2 cm and 3 cm • If the smaller divisions are 0.1 cm we know the length is between 2.8 cm and 2.9 cm • We can’t read another digit, but we can estimate how many tenths of a division past 2.8 to the arrow • We can estimate 3 tenths of a division which gives a measurement of 2.83 cm Chemistry 11 - Spectrum Community School

  46. We state the measurement as 2.83 cm. • We are certain about the first 2 digits and have some certainty about the third • eg - we know the third digit is not 0 or 9, (but it might be 2 or 4) • This measurement has 3 sig figs • We cannot write as 2.8315 because we cannot be that exact with this ruler Chemistry 11 - Spectrum Community School

  47. More than 12, less than 13 • More than 12.3, less than 12.4 • Estimated length = 12.33 cm • (4 significant figures) • Note it could also be estimated as 12.32 cm or 12.34 cm - be as accurate as you can • Any of these last 3 would be an acceptable measurement Chemistry 11 - Spectrum Community School

  48. Length is between 4 and 5 cm. Arrow is right at the 0.5 cm mark Since there is no uncertainty in the 4.5 ( it is not 4.4 or 4.6) we can report the length to 3 sig. figs. Length can be reported as 4.50 cm We know it is not 4.48 cm or 4.53 cm, but it might be 4.51 cm - some uncertainty Chemistry 11 - Spectrum Community School

  49. How many degrees Celsius? • Decide what each marked division represents • Estimate between marked divisions • Estimated temperature • Between 21 and 22 degrees C • Best estimate 21.8 degrees C • 3 sig figs Chemistry 11 - Spectrum Community School

  50. Graduated Cylinder • Estimated volume is between 20 and 30 mL (read at bottom of meniscus curve) • Large division is 5 mL, each small one is 1 mL • Estimate between 27 and 28 mL • Volume = 27.5 mL • 3 sig figs Chemistry 11 - Spectrum Community School

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