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Quantitative Analysis

Quantitative Analysis. English-Metric Conversions & Scientific Notation. Quantity – something that has magnitude, size, or amount (length, mass, volume) Unit – a quantity adopted as a standard of measurement (meter, kilogram, liter).

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Quantitative Analysis

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  1. Quantitative Analysis English-Metric Conversions & Scientific Notation

  2. Quantity – something that has magnitude, size, or amount (length, mass, volume) • Unit – a quantity adopted as a standard of measurement (meter, kilogram, liter)

  3. Conversion Factor – ratio equating two different units; used to convert from one unit to the other

  4. Density • Mass divided by volume for any substance • Often used to identify a substance • More dense objects sink to the bottom • Common conversion factor M D = V

  5. International System of Units(or SI units) –measurement system used by the scientific community worldwide Base Units are: meters, kilograms, seconds,and kelvins

  6. Page 13

  7. Length Conversions Metric to Metric 1000 millimeters (mm) = 1 meter (m) 100 centimeters (cm) = 1 meter (m) 1000 meters (m) = 1kilometer(km)

  8. English to English 1 mile (mi) = 5280 feet (ft) 1 yard (yd) = 3 feet (ft) 1 foot (ft) = 12 inches (in)

  9. Metric to English 2.54 cm = 1 in

  10. Practice Convert 12350 millimeters to miles

  11. Mass – the amount of matter in a substance • doesn’t change Weight – a force due to gravity -- can change depending on location

  12. Mass & Weight Conversions Metric to Metric 1000 milligrams (mg) = 1 gram (g) 100 centigrams (cg) = 1 gram (g) 1000 grams (g) = 1 kilogram (kg)

  13. English to English 16 ounces (oz) = 1 pound (lb) 2000 pounds (lb) = 1 ton

  14. Metric to English 453.59 g = 1 lb

  15. Practice Convert 13.5 kilograms to ounces

  16. VolumeConversions Metric to Metric 1000 milliliters (mL) = 1 liter (L) 1000 liters (L) = 1 kiloliter (kL) 1 cubic centimeter (cm3) = 1 milliliter (mL)

  17. English to English 1 gallon (gal) = 4 quarts (qt) 1 cubic foot (ft3) = 7.475 gallons (gal)

  18. Metric to English 1 L = 1.06 qt

  19. Practice Convert 6.75 cubic feet to cubic centimeters

  20. Time Conversions Universal Units 60 seconds (sec) = 1 minute (min) 60 minutes (min) = 1 hour (hr) 24 hours (hr) = 1 day 365 days = 1 year (yr) 7 days = 1 week (wk)

  21. Practice Convert 35.6 days to seconds

  22. Significant Figures How many digits does my answer have to have?! It depends on how accurate your measurements are.

  23. Nonzero digits are always significant 46.3 m has ___ sig. figs. 6.295 g has ___ sig. figs.

  24. Zeros between nonzero digits are significant 40.7 L has ___ sig. figs. 87009 km has ___ sig. figs.

  25. Zeros in front of nonzero digits are not significant 0.009587 m has ___ sig. figs. 0.0009 kg has ___ sig. figs.

  26. Zeros at the end of a number AND to the right of a decimal point are significant 85.00 g has ___ sig. figs. 9.070000000 cm has ___ sig. figs. 123000.00 mL has ___ sig. figs.

  27. Zeros at the end of a number that does not have a decimal point are not significant 8500 g has ___ sig. figs. 9070000000 cm has ___ sig. figs.

  28. Rules for using Sig. Figs. Wheredo I round off?

  29. Multiplication and division: answer has same number of sig figs as the number in problem with fewest sig. figs. 12.4 x 7.943 = 246.83 / 26 =

  30. 2. Addition and subtraction: answer can only be as accurate as the least accurate number in problem (line up your numbers) 3.95 54.638 2.879 -31.22 +213.6

  31. 3. Problems with both addition (or subtraction) and multiplication (or division): round off after each operation

  32. Converting 2 Unit Numbers • The number always goes with the unit on top • Convert top unit first, then bottom unit Convert 970 kilometers per hour to feet per second (970km/hr?ft/sec )

  33. 2 Unit Numbers as Conversion Factors • Start with the number that contains only one unit • Use the number that contains 2 units as a conversion factor in the middle of the problem

  34. Example On an average day the Delaware River flows past the Delaware Memorial Bridge at a rate of 7000 gal/sec . How many minutes would it take for 6800 kL of water to pass the Delaware Memorial Bridge?

  35. Scientific NotationConvenient way to express long numbers Rule #1 – only one non-zero digit to left of decimal Rule #2 – Large numbers have positive exponent, small numbers have negative exponent Rule #3 – move decimal right, subtract from exponent Rule #4 – move decimal left, add to exponent

  36. Practice Convert to Scientific Notation: 7538000 = 0.0000000000000896 = Convert to regular numbers: 6.97 x 10-7 = 3.21 x 1023 =

  37. Correct the following Scientific Notation: 0.0235 x 10-13 = 5635 x 10-9 = 32569 x 105 = 0.000054 x 1035 =

  38. Multiplying Multiply numbers, add exponents, correct Sci. Not. (3.1 x 103) (5.01 x 104)

  39. Multiplying Multiply numbers, add exponents, correct Sci. Not. (3.1 x 103) (5.01 x 104) (3.1 x 5.01) x 103+4

  40. Multiplying Multiply numbers, add exponents, correct Sci. Not. (3.1 x 103) (5.01 x 104) (3.1 x 5.01) x 103+4 15.531 x 107

  41. Multiplying Multiply numbers, add exponents, correct Sci. Not. (3.1 x 103) (5.01 x 104) (3.1 x 5.01) x 103+4 15.531 x 107 1.5531 x 108

  42. Multiplying Try These: (5.13 x 10-3) (9.87 x 1017) (6.58 x10-8) (1.32 x10-14)

  43. Dividing Divide numbers, subtract exponents, correct Sci. Not. 7.63 x 103= 8.62 x 104

  44. Dividing Divide numbers, subtract exponents, correct Sci. Not. 7.63 x 103=7.63x 103-4 8.62 x 104 8.62

  45. Dividing Divide numbers, subtract exponents, correct Sci. Not. 7.63 x 103=7.63x 103-4= 0.885 x 10-1 8.62 x 104 8.62

  46. Dividing Divide numbers, subtract exponents, correct Sci. Not. 7.63 x 103=7.63x 103-4= 0.885 x 10-1 8.62 x 104 8.62 0.885 x 10-1 = 8.85 x 10-2

  47. Dividing Try These, but… …watch out for double negatives when subtracting! 5.32 x 10-131.49 x 10-53.21 x 107 1.25 x 10-47 7.25 x 109 6.11 x 10-11

  48. Conversions with Sci. Not. Convert 3.24 x 108 kilometers per hour to feet per second (3.24 x 108 km/hr ? ft/sec )

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