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???

2.32.344 gg

A measurement is a quantity that has both a number and a unit.

36.36.11 mLmL 16.5 16.5 Years OldYears Old

Accuracy, Precision, and Error

Here is an example:Here is an example:

How old is my cat?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?

AccuracyAccuracy – closest to TRUE Value – closest to TRUE ValuePrecisionPrecision – repeated Same Value – 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?

The percent error is an absolute valueabsolute value (there is no positive or negative value.)

Percent Error

Percent Error = x 100% EV - AVAV

What is the percent error in your measurement of the age of my cat?

Error VS Percent ErrorWhat is Mr. Pearson’s weight? Experimental Value (EV) = 115 kgActual Value (AV) = 110 kg

= 115 kg – 110 kg x 100 % = 4.5%

Error = EV – AV

Percent Error = x 100% EV - AVAV

= 115 kg – 110 kg = 5 kg

110 kg

Error VS Percent ErrorWhat is the weight of my car? Experimental Value (EV) = 3,585 kgActual Value (AV) = 3,580 kg

= 3,585 kg – 3,580 kg x 100 % = 0.14%

Error = EV – AV

Percent Error = x 100% EV - AVAV

= 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 OceanDecimal is PRESENT

Atlantic OceanDecimal 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 RightThen count all numbers to the

Left

47.3 = __ S.F. 3

0.0021 = 2 S.F

1.200 = 4 S.F

36 = 2 S.F

2400 = 2 S.F

0.0600 = 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 mm2____S.F2 ____S.F2

5.60 L

____S.F

0.00560 kL = = 5600 mL3____S.F3 ____S.F3

= 5.60 x 103 mL

RULE-2: Every digit in scientific notation is Significant

RULE-2: Every digit in scientific notation is Significant

47.3 = 3 S.F

0.0021 = 2 S.F

1.200 = 4 S.F

36 = 2 S.F

2400 = 2 S.F

0.0600 = 3 S.F

104,000 = 3 S.F

4.73 x 101

2.1 x 10-3

1.200 x 100

3.6 x 101

2.4 x 103

6.00 x 10-2

1.04 x 105

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.FUnlimited

Sig Figs are based on the ESTIMATED Number

312 students attend GPA____S.FUnlimited

Counted = EXACT = Unlimited # of Sig FigsMeasured = 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 FigsMeasured = 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 FigsMeasured = 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. 0.00456 10–8 = 4.56 10–11

b. 454 10–8 = 4.54 10–6

c. 842.6 104 = 8.426 106

d. 0.00452 106 = 4.52 109

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 0.0130 L. How many significant figures are in this measurement?

a. 2

b. 3

c. 4

d. 5

3.1 Section Quiz