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??? 2.34 g A measurement is a quantity that has both a number and a unit mL 16.5 Years Old

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

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) Accuracy and Precision Who was more ACCURAT and more PRECISE in your measurements of the age of my cat?

Accuracy – closest to TRUE Value Precision – repeated Same 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 Error = experimental value (EV) - accepted value (AV) (measured by student) - (correct value) What is the error in your measurement of the age of my cat?

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

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

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 x 100 % = 0.14% Error = EV – AV Percent Error = x 100% EV - AV AV = 3,585 kg – 3,580 kg = 5 kg 3,580 kg

What is Mr. Pearson’s weight? Error VS Percent Error 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 % Error = 115 kg – 110 kg x 100 % = 4.5% Error = 115 kg – 110 kg = 5 kg 110 kg

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?) Significant Figures (Sig Figs) = Known + ESTIMATE

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

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.

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

37 m ____S.F Sig Fig Rules: Is the decimal PRESENT or ABSENT PRESENT ABSENT.037 km = = 37,000 mm 2 ____S.F L ____S.F kL = = 5600 mL 3 ____S.F 3 3 = 5.60 x 10 3 mL RULE-2: Every digit in scientific notation is Significant

47.3 = 3 S.F = 2 S.F = 4 S.F 36 = 2 S.F 2400 = 2 S.F = 3 S.F 104,000 = 3 S.F 4.73 x x x x x x x 10 5

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 ____S.F Unlimited Sig Figs are based on the ESTIMATED Number 312 students attend GPA ____S.F Unlimited 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) _ 3 sig figs Most certainty and greatest PRECISION Counted = EXACT = Unlimited # of Sig Figs Measured = ESTIMATED = Certain # of Sig Figs

Sig Fig Rules: Is the decimal PRESENT or ABSENT PRESENT ABSENT 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

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. = __ S.F = 5 S.F = 4 S.F = 5 S.F = Unlimited = 2 S.F 3

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

3.2

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

3.3

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

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? a  10 –8 = 4.56  10 –11 b.454  10 –8 = 4.54  10 –6 c  10 4 =  10 6 d  10 6 = 4.52  10 9

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

3. A student reports the volume of a liquid as L. How many significant figures are in this measurement? a.2 b.3 c.4 d Section Quiz