Transcript Accuracy, Percision, Error, and Sig Figs

A measurement is a quantity that
has both a number and a unit.
2.34 g
36.1 mL
16.5 Years Old
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???
Accuracy, Precision, and Error
How do you evaluate accuracy and
precision? (Your thoughts???)
Here is an example:
How old is my cat?
_____ Months
(everyone must guess)
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?
Accuracy – closest to TRUE Value
Precision – repeated Same Value
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?
Percent Error
Percent Error = EV - AV x 100%
AV
The percent error is an absolute value
(there is no positive or negative value.)
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
Error = EV – AV = 115 kg – 110 kg =
5 kg
Percent Error = EV - AV x 100%
AV
= 115 kg – 110 kg x 100 % =
110 kg
4.5%
Error
VS
Percent Error
What is the weight of my car?
Experimental Value (EV) = 3,585 kg
Actual Value (AV) = 3,580 kg
Error = EV – AV = 3,585 kg – 3,580 kg =
5 kg
Percent Error = EV - AV x 100%
AV
= 3,585 kg – 3,580 kg x 100 % =
3,580 kg
0.14%
Error
VS
Percent Error
What is Mr. Pearson’s weight?
Error = 115 kg – 110 kg = 5 kg
% Error = 115 kg – 110 kg x 100 % =
110 kg
4.5%
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 % =
3,580 kg
0.14%
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?)
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)
3 sig figs
Most certainty
and greatest
PRECISION
Which measurement has the 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
47.3 = __
3 S.F.
0.0021 = 2 S.F
1.200 = 4 S.F
36
Atlantic Ocean
Decimal is
ABSENT
= 2 S.F
Find the first
Find the first
NON-Zero
NON-Zero
2400 = 2 S.F
number starting
number starting
0.0600 = 3 S.F
from the Right
from the Left
Then count all 104,000 = 3 S.F Then count all
numbers to the
numbers to the
Left
Right
Do not start writing/copying until I tell you
Sig Fig Rules: Is the decimal PRESENT or ABSENT
ABSENT
PRESENT
.037 km
2
____S.F
=
=
37 m
2
____S.F
37,000 mm
2
____S.F
0.00560 kL
3
____S.F
=
5.60 L =
3
____S.F
5600 mL
3
____S.F
= 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
0.0021
1.200
4.73 x 101 = 3 S.F
2.1 x 10-3
= 2 S.F
1.200 x 100 = 4 S.F
36
3.6 x 101
= 2 S.F
2400
2.4 x 103
= 2 S.F
0.0600
6.00 x 10-2 = 3 S.F
104,000
1.04 x 105
= 3 S.F
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
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
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
3 S.F
= __
= 5 S.F
= 4 S.F
= 5 S.F
= Unlimited
= 2 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.
for Sample Problem 3.1
Problem Solving 3.3 Solve Problem 3
with the help of an interactive guided
tutorial.
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
3.1 Section Quiz
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