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SCIENTIFIC MEASUREMENT

SCIENTIFIC MEASUREMENT. Measurements in the Lab:. 23°C. 23°C. The number of SFs in a measured value is equal to the number of known digits plus one uncertain digit. 22°C. 22°C. 21°C. 21°C. you record 21.6°C. you record 21.68°C. Measurements in the Lab:. Example B. Example A.

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SCIENTIFIC MEASUREMENT

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  1. SCIENTIFIC MEASUREMENT

  2. Measurements in the Lab: 23°C 23°C The number of SFs in a measured value is equal to the number of known digits plus one uncertain digit. 22°C 22°C 21°C 21°C you record 21.6°C you record 21.68°C

  3. Measurements in the Lab: Example B Example A 1. If the glassware is marked every 10 mLs, the volume you record should be in mLs. (Example A) 2. If the glassware is marked every 1 mL, the volume you record should be in tenths of mLs. 3. If the glassware is marked every 0.1 mL, the volume you record should be in hundredths of mLs. (Example B) 0 mL 30 mL 20 mL 1 mL 10 mL 30-mL beaker: the volume you write in your lab report should be 13 mL 2 mL Buret marked in 0.1 mL: you record volume as 0.67 mL

  4. Cheap balance measurements are trustworthy to the nearest gram. Measurement = 25 g, so implied precision is +/-1g. Standard lab balance are trustworthy to the nearest milligram (0.001g) measurement: 25.000g, so implied precision is +/-0.001g The analytical balance is very precise. Measurements are trustworthy to the nearest 0.1mg. Measurement:25.0000 implied precision: +/-0001g

  5. Reporting Measurements • Using significant figures • Report what is known with certainty • Add ONE digit of uncertainty (estimation) Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

  6. How good are the measurements? (that’s where sig fig’s come in!) • Scientists use two word to describe how good the measurements are • Accuracy- how close the measurement is to the actual value • Precision- how well can the measurement be repeated • In short, when you plug these three numbers into your calculator, remember your calculator neither knows nor cares about how good (significant) the numbers it’s working with are. However, to you, the taker of data, these three numbers tell you whether or not your data is good enough to pay attention to.

  7. Significant Figures are concerned with Accuracy vs. Precision in measurement Poor accuracy Poor precision Good accuracy Good precision Poor accuracy Good precision Random errors: reduce precision Systematic errors: reduce accuracy

  8. Differences • Accuracy can be true of an individual measurement or the average of several • Precision requires several measurements before anything can be said about it

  9. Let’s use a golf analogy

  10. Accurate? No Precise? Yes 10

  11. Precise? Yes Accurate? Yes 12

  12. Accurate? Maybe? Precise? No 13

  13. Precise? We cant say! Accurate? Yes 18

  14. Precise? We cant say! Accurate? Yes 18

  15. Precise? We cant say! Accurate? Yes 18

  16. not accurate, not precise accurate, not precise not accurate, precise accurate and precise accurate, low resolution 3 2 1 time offset [arbitrary units] 0 -1 -2 -3 Accuracy Precision Resolution subsequent samples

  17. Significant figures • Using proper significant figures in measured and calculated values conveys a sense of precision to the reader and defines a limit of error in the value.

  18. Significant figures are all the digits in a measurement that are known with certainty plus a last digit that must be estimated

  19. 1 2 3 4 5 0 cm 1 2 3 4 5 0 cm 1 2 3 4 5 0 cm Practice Measuring 4.5 cm 4.54 cm 3.0 cm Timberlake, Chemistry 7th Edition, page 7

  20. Using Significant Figures reflects precision by estimating the last digit • What is the certain measurement? • What is the estimated measurement?

  21. The instrument determines the amount of precision of the data. • What is the certain measurement here? • What is the estimated measurement here?

  22. Error vs. Mistakes ERROR MISTAKES Mistakes are caused by PEOPLE Misreading, dropping, or other human mistakes are NOT error • Scientific errors are caused by INSTRUMENTS • Scientific measurements vary in their level of certainty

  23. Significant Figures • What is the smallest mark on the ruler that measures 142.15 cm? • 142 cm? • 140 cm? • Here there’s a problem, does the zero count or not? • They needed a set of rules to decide which zeros count. (Non-zeros always count)

  24. SIG FIG Rules • Rule one • All non zero numbers are significant! • PRACTICE • 245.36 g • 2 g • 6.4 g • 428999999 g

  25. SIG FIG Rules • Rule two • All zeros between significant figures are significant • So if the zeros are sandwiched or embedded in the number they ARE significant • PRACTICE • 5004 g • 62.0003 g • 20.03 g • 2.06004 g

  26. SIG FIG Rules • Rule three • All trailing zeros to the right of the decimal ONLY are significant • Those at the end of a number without the decimal point don’t count • Practice • 42.00000 g • 0.3300 g • 50000 g • 50.0000 g • 200.002200 g • 0.0000040 g

  27. Which zeros count? • If the number is smaller than one, zeros before the first number don’t count • 0.045 g • Zeros between other sig figs do. • 1002 g • zeroes at the end of a number after the decimal point do count • 45.8300 g • If they are holding places, they don’t. • 0.0006 g • If measured (or estimated) they do count

  28. Another way to figure it out • If the number has a decimal in it: • Find the first non zero from the LEFT • That is the first significant figure in the number, and all digits after (as you move toward the right) ARE significant • PRACTICE: • 3.4000000 g • 0.00003420 g • 404.0 g • 0.1100000 g • 30000 g

  29. If the number does NOT have a decimal in it: • Find the first non zero from the RIGHT • That is the first significant figure in the number, and all digits after (as you move toward the left) ARE significant. • Practice • 560000 g • 20000020 g • 2002.00 g • 3030300 g

  30. Exact and Counting Numbers do not have significant digits

  31. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • Ex: • A dozen is exactly 12 • Number of students in this classroom • Unit conversions in most cases will be considered exact numbers • Ex: • 1 milliliter is exactly .001 of a liter • 100 centimeters is exactly 1 meter

  32. Sig figs. • How many sig figs in the following measurements? • 458 g • 4000085 g • 4850 g • 0.0485 g • 0.0040850 g • 40.004085 g

  33. Sig Figs. • 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.0500060 g • Next we learn the rules for calculations

  34. Calculations with sig figs • The answer can’t be more precise than the question

  35. Calculations • Addition/Subtraction • The answer is based on the number with the fewest decimal points • Multiplication/Division • The answer is based on the number with the fewest significant digits

  36. Calculations Involving Measured Data • Addition/Subtraction: • The answer contains the same number of digits to the right of the decimal as that of the measurement with the fewest number of decimal places. 3.14159 g + 25.2 g 28.34159 g 28.3 g 3 SFs 33.14159 g - 33.04 g 0.10159 g 0.10 g 2 SFs • Calculators do NOT know these rules. It’s up to you to apply them!

  37. For example 27.93 + 6.4 27.93 27.93 + 6.4 6.4 1. First line up the decimal places 2. Then do the adding 3. Count the sig figs in the decimal portion of each addend. 34.33 4. Round your answer to the place value of the addend with the least number of decimal places

  38. Rounding rules • look at the number to the right of place you are rounding to. • If it is 0 to 4 don’t change it • If it is 5 to 9 make it one bigger • round 45.462 to four sig figs • to three sig figs • to two sig figs • to one sig fig

  39. Practice • 4.8 g + 6.8765 g • 520 cm + 94.98 cm • 0.0045 m + 2.113 m • 6.0 x 102 L - 3.8 x 103 L • 5.4 ml - 3.28 ml • 6.7 g - .542 g • 500 cm -126 cm • 6.0 x 10-2 mg - 3.8 x 10-3 mg

  40. Multiplication and Division • Same number of sig figs in the answer as the least in the question • 3.6 g x 653 g • 2350.8 g is the answer you would get in your calculator • 3.6 has 2 s.f. 653 has 3 s.f. • So your answer can only have 2 s.f. • You must round to 2 sig figs and your answer is 2400 g

  41. Multiplying or Dividing Measured Data • answer contains the same number of SFs as the measurement with the fewest SFs. 25.2 m x 6.1 m = 153.72 m (on my calculator) = 1.5 x 102 m (correct answer) 25.2 g ------------ = 7.3122535 g 3.44627 g = 7.31 g (correct answer) (6.626 x 10-34)(3 x 108) ------------------------------- = 3.06759 x 10-2 (on my calculator) 6.48 x 10-24 = 0.03 (correct answer)

  42. Multiplication and Division • Same rules for division • practice • 4.5 g / 6.245 g • 4.5 m x 6.245 m • 9.8764 L x .043 L • 3.876 mg / 1983 mg • 16547 g / 714 g

  43. QUANTITATIVE MEASUREMENTS • Described with a value (number) & a unit (reference scale) • Both the value and unit are of equal importance!! NO NAKED NUMBERS!!!!!!!!!!

  44. Problems • 50 is only 1 significant figure, but if I actually measured or estimated the ones place value to be 0, it really has two significant figures. How can I write it? • A zero at the end only counts after the decimal place • So, I can use Scientific notation • 5.0 x 101 • now the zero counts.

  45. SCIENTIFIC NOTATION Based on Powers of 10 Technique Used to 1. Express Very Large or Very Small Numbers 2. Reduce likely-hood of errors 3. Compare Numbers Written in Scientific Notation • First Compare Exponents of 10 (order of magnitude) • Then Compare Numbers

  46. SCIENTIFIC NOTATION Numbers that are very small The electrical charge on one electron: 0.0000000000000000001602 = 1.602 X 10-19 C

  47. Or numbers that are very big!! The mass of the moon: 73,600,000,000,000,000,000,000 kg = 7.36 X 1022kg

  48. SCIENTIFIC NOTATION • Writing Numbers in Scientific Notation • Locate the Decimal Point • Move the decimal point just to the right of the non-zero digit in the largest place • The new number is now greater than one but less than ten • Multiply the new number by 10n • where n is the number of places you moved the decimal point • Determine the sign on the exponent, n • If the decimal point was moved left, n is + • If the decimal point was moved right, n is – • If the decimal point was not moved, n is 0

  49. Practice writing in scientific notation • 46600000 = 4.66 x 107 • 0.00053 = 5.3 x 10-4 • 123,000,000,000 = 1.23 x 1011

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