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Scientific Measurement

Scientific Measurement. Measurement. In chemistry, #’s are either very small or very large 1 gram of hydrogen = 602,000,000,000,000,000,000,000 atoms Mass of an atom of gold = 0.000 000 000 000 000 000 000 327 gram. Scientific Notation.

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Scientific Measurement

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  1. Scientific Measurement www.assignmentpoint.com

  2. Measurement In chemistry, #’s are either very small or very large 1 gram of hydrogen = 602,000,000,000,000,000,000,000 atoms Mass of an atom of gold = 0.000 000 000 000 000 000 000 327 gram www.assignmentpoint.com

  3. Scientific Notation • Condensed form of writing large or small numbers • When a given number is written as the product of 2 numbers • M x 10n • M must be: • greater than or equal to 1 • less than 10 • n must be: • whole number • positive or negative www.assignmentpoint.com

  4. Find M by moving the decimal point over in the original numberto the • left or right so that only one non-zero • number is to the left of the decimal. www.assignmentpoint.com

  5. Find n by counting the number of places you moved the decimal: To the left (+) or To the right (-) www.assignmentpoint.com

  6. Scientific Notation Examples • 20 = • 200 = • 501 = • 2000 = 2.0 x 101 2.0 x 102 5.01 x 102 2.000 x 103 www.assignmentpoint.com

  7. More examples… 3 x 10-1 • 0.3 = • 0.21 = • 0.06 = • 0.0002 = • 0.000314 = Rule: If a number starts out as < 1, the exponent is always negative. 2.1 x 10-1 6 x 10-2 2 x 10-4 3.14 x 10-4 www.assignmentpoint.com

  8. Scientific Notation • Adding & Subtracting: • if they have the same n, just add or subtract the M values and keep same n • if they don’t have the same n, change them so they do www.assignmentpoint.com

  9. Scientific Notation • Multiplying: • the M values are multiplied • the n values are added www.assignmentpoint.com

  10. Scientific Notation • Division: • the M values are divided • the n values are subtracted www.assignmentpoint.com

  11. Accuracy & Precision ‘How close you are really counts!’ www.assignmentpoint.com

  12. Accuracy • Accuracy – a measure of how close a measurement comes to the actual or true value of what is measured To evaluate… the measured value must be compared to the correct value www.assignmentpoint.com

  13. Precision • Precision – a measure of how close a series of measurements are to one another To evaluate… you must compare the values of 2 or more repeated measurements www.assignmentpoint.com

  14. Accuracy vs. Precision www.assignmentpoint.com

  15. Errors are Unavoidable • Measuring instruments have limitations • Hence, there will always be errors in measurement. www.assignmentpoint.com

  16. Not All Errors are Equal • You are an eye surgeon • Consider the following two errors: • You fly from NY to San Francisco • Your plane is blown off course by 3cm • Your scalpel misses the • mark by 3cm The errors sound equal… but are they? www.assignmentpoint.com

  17. Absolute Error • The error in each of the previous examples is 3cm • But the error in each is not equivalent! • This type of error is the absolute error. Absolute error = | measured value – accepted value | • Accepted value is the most probable value or the value based on references • Only the size of the error matters, not the sign www.assignmentpoint.com

  18. Significance of an Error • The absolute error tells you how far you are from the accepted value • It does not tell you how significant the error is. • Being 3cm off course on a trip to San Francisco is insignificant because the city of San Francisco is very large. • Being 3cm off if you are an eye surgeon means your operating on the wrong eye! • It is necessary to compare the size of the error to the size of what is being measured to understand the significance of the error. www.assignmentpoint.com

  19. Percentage Error • The percentage error compares the absolute error to the size of what is being measured. % error =|measured value – accepted value| x 100% accepted value www.assignmentpoint.com

  20. Sample Problem • Example:Measuring the boiling point of H2O Thermometer reads – 99.1OC You know it should read – 100OC Error = measured value – accepted value % error = |error| x 100% accepted value www.assignmentpoint.com

  21. C C % error = |99.1oC – 100.0oC| x 100% 100oC = 0.9o x 100% 100o = 0.009 x 100% = 0.9% www.assignmentpoint.com

  22. Significant Figures • Used as a way to express which numbers are known with certainty and which are estimated www.assignmentpoint.com

  23. What are significant figures? Significant Figures – all the digits that are known, plus a last digit that is estimated www.assignmentpoint.com

  24. Rules 3 sig figs 1) All digits 1-9 aresignificant Example: 129 2) Embedded zeros between significant digits are always significant Example: 5,007 3) Trailing zeros in a number are significant only if the number contains a decimal point Example: 100.0 3600 4 sig figs 4 sig figs 2 sig figs www.assignmentpoint.com

  25. 2 sig figs 4) Leading zeros at the beginning of a number are never significant Example: 0.0025 5) Zeros following a decimal significant figure arealways significant Example: 0.000470 0.47000 6) Exceptions to the rule are numbers with an unlimited number of sig figs Example = Counting – 25 students Exact quantities – 1hr = 60min, 100cm = 1m 3 sig figs 5 sig figs www.assignmentpoint.com

  26. Significant Figure Examples 3 5 • 123m = • 9.8000 x 104m = • 0.070 80 = • 40, 506 = • 22 meter sticks = • 98, 000 = • 143 grams = • 0.000 73m = • 8.750 x 10-2g = 4 5 unlimited 2 3 2 4 www.assignmentpoint.com

  27. Calculations Using Significant Figures • Rounding 1st determine the number of sig figs Then, count from the left, & round If the digit < 5, the value remains the same. If the digit is ≥ 5, the value of the last sig fig is increased by 1. www.assignmentpoint.com

  28. Try your hand at rounding… • Round each measurement to 3 sig figs. • 87.073 meters = • 4.3621 x 108 meters = • 0.01552 meter = • 9009 meters = • 1.7777 x 10-3 meter = • 629.55 meters = 87.1m 4.36 x 108 m 0.0155m or 1.55 x 10-2m 9010m 1.78 x 10-3m 630. m or 6.30 x 102m www.assignmentpoint.com

  29. Multiplyingand Dividing Limit and round to the least number of significant figures in any of the factors. 23.0cm x 432cm x 19cm = Answer = Because 19 only has 2 sig figs 188,784cm3 190,000cm3 or 1.9 x 103cm3 www.assignmentpoint.com

  30. Addition and Subtraction Limit and round your answer to leastnumber of decimal places in any of the numbers that make up your answer. 123.25mL + 46.0mL + 86.257mL = Answer = Because 46.0 has only 1 decimal place 255.507mL 255.5mL www.assignmentpoint.com

  31. The International System of Units www.assignmentpoint.com

  32. Based on the #10 • Makes conversions easier • Old name = metric system www.assignmentpoint.com

  33. Units and Quantities • Length – the distance between 2 points or objects Base unit = meter • Volume – the space occupied by any sample of matter V = length x width x height Base unit = liter Based on a 10cm cube (10cm x 10cm x 10cm = 1000cm3) 1 liter = 1000cm3 www.assignmentpoint.com

  34. Mass – the amount of matter contained in an object Base unit = gram Different than weight… Weight - a force that measures the pull of gravity www.assignmentpoint.com

  35. www.assignmentpoint.com

  36. Temperature – a measure of the energy of motion How fast are the molecules moving? When 2 objects are at different temperatures heat is always transferred from the warmer → the colder object www.assignmentpoint.com

  37. Temperature Scales • Celsius scale – Freezing point of H2O = 0oC Boiling point of H2O = 100oC • Kelvin scale – Freezing point of H2O = 273.15K Boiling point of H2O = 373.15K K = C + 273 C = K - 273 www.assignmentpoint.com

  38. Temperature Scale Conversions www.assignmentpoint.com

  39. Conversion FactorsandUnit Cancellation www.assignmentpoint.com

  40. A physical quantity must include: Number + Unit www.assignmentpoint.com

  41. 1 foot = 12 inches www.assignmentpoint.com

  42. 1 foot = 12 inches 1 foot =1 12 inches www.assignmentpoint.com

  43. 1 foot = 12 inches 1 foot =1 12 inches 12 inches =1 1 foot www.assignmentpoint.com

  44. 1 foot 12 inches 12 inches 1 foot “Conversion factors” www.assignmentpoint.com

  45. 1 foot 12 inches 12 inches 1 foot “Conversion factors” How many inches are in 3 feet? 12 inches ( ) ( ) =36 inches 3 feet 1 foot www.assignmentpoint.com

  46. 100 cm ______ 100 cm 1 m ______ 1 m 1 m 100 cm ______ 132 cm ( ) equality: 1 m = 100 cm conversion factors: How many cm are in 1.32 meters? or X cm = 1.32 m = We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose. www.assignmentpoint.com

  47. 0.0872 m 100 cm ______ 1 m ______ 1 m 100 cm ______ ( ) 1 m 100 cm equality: 1 m = 100 cm conversion factors: How many meters is 8.72 cm? or X m = 8.72 cm = Again, the units must cancel. www.assignmentpoint.com

  48. 1 ft ______ 1 ft 12 in 12 in ( ) 12 in ______ ____ 1 ft 3.28 ft equality: 1 ft = 12 in How many feet is 39.37 inches? conversion factors: or X ft = 39.37 in = Again, the units must cancel. www.assignmentpoint.com

  49. 1 km 1,000 m ( ) ______ ( ) ____ 1 m 10 dm 1.5 km How many kilometers is 15,000 decimeters? X km = 15,000 dm = www.assignmentpoint.com

  50. ( ) _____ 60 min 1 h 378,432 s ( ) ( ) ____ 60 s 3.78 x 105 s ____ 24 h 1 min 1 d How many seconds is 4.38 days? X s = 4.38 d = If we are accounting for significant figures, we would change this to… www.assignmentpoint.com

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