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2.3 4 g

A measurement is a quantity that has both a number and a unit. Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to MAKE measurements and to decide whether a measurement is CORRECT .

cameron-bullock
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2.3 4 g

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  1. A measurement is a quantity that has both a number and a unit. • Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to MAKE measurements and to decide whether a measurement is CORRECT. • -- Are you “certain” that your measurement is correct? HOW “certain” are you??? 2.34g 36.1mL 16.5 Years Old

  2. How do you evaluate accuracy and precision? (Your thoughts???) • Accuracy, Precision, and Error Here is an example: How old is my cat? _____ Months (everyone must guess)

  3. Accuracy and Precision • Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. (closest to TRUE Value) • Precision is a measure of how close a series of measurements are to one another. (repeated Save Value) • Who was more ACCURAT and more PRECISE in your measurements of the age of my cat?

  4. Accuracy – closest to TRUE Value Precision – repeated Same Value

  5. Error = experimental value (EV) - accepted value (AV) (measured by student) - (correct value) • Determining Error • The experimental value (EV) is the value measured in the lab. (by the student) • The accepted value (AV) is the correct value based on reliable references. • The error is the difference between the experimental value and the accepted value • What is the error in your measurement of the age of my cat?

  6. Percent Error • The percent error is an absolute value (there is no positive or negative value.) EV - AV Percent Error = x 100% AV • What is the percent error in your measurement of the age of my cat?

  7. Error VS Percent Error • What is Mr. Pearson’s weight? • Experimental Value (EV) = 115 kg • Actual Value (AV) = 110 kg • = 115 kg – 110 kg = 5 kg EV - AV • Error = EV – AV Percent Error = x 100% AV • = 115 kg – 110 kg x 100 % = 4.5% • 110 kg

  8. Error VS Percent Error • What is the weight of my car? • Experimental Value (EV) = 3,585 kg • Actual Value (AV) = 3,580 kg • = 3,585 kg – 3,580 kg = 5 kg EV - AV • Error = EV – AV Percent Error = x 100% AV • = 3,585 kg – 3,580 kg x 100 % = 0.14% • 3,580 kg

  9. Error VS Percent Error • What is Mr. Pearson’s weight? • Error = 115 kg – 110 kg = 5 kg • % Error = 115 kg – 110 kg x 100 % = 4.5% • 110 kg • What is the weight of my car? • Error = 3,585 kg – 3,580 kg = 5 kg • % Error = 3,585 kg – 3,580 kg x 100 % = 0.14% • 3,580 kg

  10. Significant Figures (Sig Figs) =Known+ESTIMATE • The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. • Significant Figures relate to the certainty of a measurement – The PRECISION of the measurement • (If you are buying something that costs $1,000,000 per centimeter how certain (how PRECISE) do you want your measurement to be?)

  11. Precision = Same REPEATABLE Value (Certainty) More Sig Figs = more certainty = greater precision • _ 1 sig fig (.6 is the estimate) • _ 2 sig figs (.01 is the estimate) • Most certainty and greatest PRECISION • _ 3 sig figs • Which measurement has the most certainty and greatest PRECISION?

  12. Guesses only, don’t write any of this down YET. • There are rules (hints) to help you in determining the number of significant figures there are in a measurement.

  13. Sig Fig Rules: Is the decimal PRESENT or ABSENT 47.3 = __ S.F. 3 Atlantic Ocean Decimal is ABSENT Pacific Ocean Decimal is PRESENT 0.0021 = 2 S.F 1.200 = 4 S.F 36 = 2 S.F Find the firstNON-Zero number starting from the Right Then count all numbers to the Left Find the firstNON-Zero number starting from the Left Then count all numbers to the Right 2400 = 2 S.F 0.0600 = 3 S.F = 3 S.F 104,000 Do not start writing/copying until I tell you

  14. Sig Fig Rules: Is the decimal PRESENT or ABSENT ABSENT PRESENT = 37,000 mm .037 km = 37 m 2 2 2 ____S.F ____S.F ____S.F = 5600 mL 0.00560 kL = 5.60 L 3 3 3 ____S.F ____S.F ____S.F = 5.60 x 103 mL RULE-2: Every digit in scientific notation is Significant

  15. RULE-2: Every digit in scientific notation is Significant = 3 S.F 4.73 x 101 47.3 = 2 S.F 0.0021 2.1 x 10-3 1.200 1.200 x 100 = 4 S.F 3.6 x 101 36 = 2 S.F = 2 S.F 2400 2.4 x 103 = 3 S.F 6.00 x 10-2 0.0600 = 3 S.F 1.04 x 105 104,000

  16. RULE-3: Any number that is counted is an EXACT number and has UNLIMITED significant digits. There is no ESTIMATED number. I have three cats = 3 Cats Unlimited ____S.F Sig Figs are based on the ESTIMATED Number 312 students attend GPA Unlimited ____S.F Counted = EXACT = Unlimited # of Sig Figs Measured = ESTIMATED = Certain # of Sig Figs

  17. Counted = EXACT = Unlimited # of Sig Figs Measured = ESTIMATED = Certain # of Sig Figs • _ 1 sig fig (.6 is the estimate) • _ 2 sig figs (.01 is the estimate) • Most certainty and greatest PRECISION • _ 3 sig figs

  18. Sig Fig Rules: Is the decimal PRESENT or ABSENT ABSENT PRESENT RULE-2: Every digit in scientific notation is Significant RULE-3: Any number that is counted is an EXACT number and has unlimited significant digits. There is no ESTIMATED number. Counted = EXACT = Unlimited # of Sig Figs Measured = ESTIMATED = Certain # of Sig Figs

  19. 3 = __ S.F = 5 S.F = 5 S.F = Unlimited = 2 S.F = 4 S.F • Guesses only, don’t write any of this down YET. • There are rules (hints) to help you in determining the number of significant figures there are in a measurement.

  20. for Sample Problem 3.1 Problem Solving 3.3 Solve Problem 3 with the help of an interactive guided tutorial.

  21. 3.2

  22. for Sample Problem 3.2 Problem Solving 3.6 Solve Problem 6 with the help of an interactive guided tutorial.

  23. 3.3

  24. for Sample Problem 3.3 Problem Solving 3.8 Solve Problem 8 with the help of an interactive guided tutorial.

  25. 3.1 Section Quiz • 1. In which of the following expressions is the number on the left NOT equal to the number on the right? • 0.00456  10–8 = 4.56  10–11 • 454  10–8 = 4.54  10–6 • 842.6  104 = 8.426  106 • 0.00452  106 = 4.52  109

  26. 3.1 Section Quiz • 2. Which set of measurements of a 2.00-g standard is the most precise? • 2.00 g, 2.01 g, 1.98 g • 2.10 g, 2.00 g, 2.20 g • 2.02 g, 2.03 g, 2.04 g • 1.50 g, 2.00 g, 2.50 g

  27. 3.1 Section Quiz • 3. A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement? • 2 • 3 • 4 • 5

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