Download Accuracy, Precision and Significant Figures PPT

Section 5.2
Uncertainty in Measurement and Significant Figures
Objectives
1. To learn how uncertainty in a measurement arises
2. To learn to indicate a measurement’s uncertainty by
using significant figures
3. To learn to determine the number of significant figures
in a calculated result
4. To learn the difference between accuracy and precision
of a measurement
Section 5.2
Uncertainty in Measurement and Significant Figures
A. Uncertainty in Measurement
• A measurement always has some degree of uncertainty.
– How long is this nail?
Section 5.2
Uncertainty in Measurement and Significant Figures
A. Uncertainty in Measurement
• Different people estimate differently.
• Record all certain numbers and one estimated number.
• Whenever we measure in chemistry we always record
one extra decimal place (estimated number) beyond the
markings on the measurement device.
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
• Numbers recorded in a measurement.
– All the certain numbers plus the first estimated number
• Accuracy of a measurement – how close your number comes to the
actual value
– similar to hitting the bull's-eye on a dart board
• Precision of a measurement – how close your repeated
measurements come to each other (not necessarily the actual
value)
– how closely grouped are your 3 darts on the board (even if
they’re not close to the bull's-eye)
• It is possible for measurements to be precise but not accurate, just
as it is possible to be accurate but not precise
Section 5.2
Uncertainty in Measurement and Significant Figures
• Accuracy and Precision
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Counting Significant Figures (Simple Method)
1. If the number has a decimal point, attack it from the left;
if the number has no decimal point, attack it from the
right.
2. Pass through all zeros until you hit the first non-zero
number
• The zeros you passed through are NOT significant
digits!
3. Every number you encounter from now on is a
significant digit!
• Including any zeros!
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Counting Significant Figures (Simple Method)
Pacific
Atlantic
if a number
has a Period
(decimal),
come from
the Pacific
side
if a period
(decimal) is
Absent,
come from
the Atlantic
side
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Counting Significant Figures (Simple Method)
•
•
•
•
•
•
•
•
•
•
100
410100
100.
100.8
100.80
0.00287
0.002870
1.0805 x 104
1.0805 x 10-12
1.205670 x 10-6
attack from _____
attack from _____
attack from _____
attack from _____
attack from _____
attack from _____
attack from _____
attack from _____
attack from _____
attack from _____
__ sig figs
__ sig figs
__ sig figs
__ sig figs
__ sig figs
__ sig figs
__ sig figs
__ sig figs
__ sig figs
__ sig figs
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Counting Significant Figures (Hard Method)
1. Nonzero integers always count as significant figures.
1457
4 significant figures
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Counting Significant Figures (Hard Method)
2. Zeros
a. Leading zeros - never count
0.0025
2 significant figures
b. Captive zeros - always count
1.008
4 significant figures
c. Trailing zeros - count only if the number is written
with a decimal point
100
1 significant figure
100.
3 significant figures
120.0 4 significant figures
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Counting Significant Figures (Both Methods)
3. Exact numbers - unlimited significant figures
• Exact counts have unlimited (infinite) sig figs; they are
obtained by simple counting (no uncertainty):
• 3 apples, 12 eggs, 1 mole
• Conversion Factors have unlimited sig figs also:
• 1 in. = 2.54 cm
• 1 mole = 6.022 x 1023 atoms
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Multiplication and Division
• The number of significant figures in the answer is the
same as in the measurement with the smallest number
of significant figures.
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Addition and Subtraction
• The number of decimal places in the result is the same
as in the measurement with the smallest number of
decimal places (not sig figs!).
Section 5.2
Uncertainty in Measurement and Significant Figures
B. Significant Figures
Rules for Counting Significant Figures
VITALLY IMPORTANT:
•
For the rest of the year, all calculations must include the
correct number of significant figures in order to be fully
correct!
– on all homework, labs, quizzes, and tests, etc.
– even if the directions don’t specifically tell you so