Accuracy & Precision
Two important points in measurement
Accuracy and Precision
At the conclusion of our time
together, you should be able to:
1. Explain the difference between the accuracy
and precision
2. Give examples of accuracy and precision
Accuracy

Accuracy = the extent to which a
measured value agrees with a standard
value
 Accuracy of a device must be checked
 Does it read a proper accepted value?

Beware of Parallax – the apparent shift
in position when viewed at a different
angle.
Graduated Cylinder –
Meniscus and Parallax
Example: Accuracy
 Who
is more accurate when measuring a book
that has a true length of 17.0 cm?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm
Murphy's Laws
of
Science and Technology
Technology is dominated by those who manage
what they do not understand.
Precision
Precision = the degree of exactness of
a measurement that is repeatedly
recorded.
 Which set is more precise?
18.2 , 18.4 , 18.35
17.9 , 18.3 , 18.85
16.8 , 17.2 , 19.44

Example: Precision
Who is more precise when measuring the same
17.0 cm book?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm
Accuracy vs. Precision
High Accuracy
High Precision
High Precision
Low Accuracy
Can you hit the bull's-eye?
Three
targets with
three
arrows each
to shoot.
How do
they
compare?
Both
accurate
and
precise
Precise
but not
accurate
Neither
accurate
nor
precise
Can you define accuracy vs. precision?
Why Is There Uncertainty?
• Measurements are performed with instruments,
and no instrument can read to an infinite number of
decimal places
•Which of the instruments below has the greatest
uncertainty in measurement?
The Scientific Method
begins with
Questions about the World Around You.
Ever Wonder Why?...
Braille dots are on the keypads of drive-up
ATM's?
Accuracy and Precision
Let’s see if you can:
1. Explain the difference between the accuracy
and precision
2. Give examples of accuracy and precision
Exit Quiz: Evaluate whether the
following are precise, accurate or both.
Low Accuracy
Low Accuracy
High
Accuracy
Low Precision
High Precision
High
Significant Figures
In Measurements
Significant Figures
At the conclusion of our time
together, you should be able to:
1. Explain what significant figures are in a
measurement
2. Determine the number of significant figures
in any measurement
Significant Figures
The significant figures in a measurement include all
of the digits that are known, plus one last digit
that is estimated.
The numbers reported in a measurement are
limited by the measuring tool.
How many sig figs are there in a
given measurement?
Measurement and Significant
Figures




Every experimental
measurement has a degree
of uncertainty.
The volume, V, at right is
certain in the 10’s place,
10mL<V<20mL
The 1’s digit is also certain,
17mL<V<18mL
A best guess is needed for
the tenths place.




To indicate the precision of a measurement,
the value recorded should use all the digits
known with certainty, plus one additional
estimated digit that usually is considered
uncertain by plus or minus 1.
No further insignificant digits should be
recorded.
The total number of digits used to express
such a measurement is called the number of
significant figures.
All but one of the significant figures are
known with certainty. The last significant
figure is only the best possible estimate.
Below are two measurements of the
mass of the same object. The same
quantity is being described at two
different levels of precision or
certainty.
15 Helpful Hints On The Lab Report from
Mr. T’s Vast Lab Experience!!!
Hint #5. A record of data is essential. It
fools the instructor into thinking that you
were working.
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
First digit (known)
= 2
cm
2.?? cm
Second digit (known) = 0.7
2.7? cm
Third digit (estimated) between
0.05- 0.08 cm
Length reported
2.77 cm
=
or
2.76 cm
or
2.78 cm
Known + Estimated Digits
In 2.77 cm…
• Known digits 2 and 7 are 100% certain
• The third digit 7 is estimated (uncertain)
• In the reported length, all three digits
(2.77 cm) are significant including the
estimated one
Learning Check
. l8. . . . I . . . . I9. . . . I . . . . I10. .
What is the length of the line?
1) 9.31 cm
2) 9.32 cm
3) 9.33 cm
How does your answer compare with your
neighbor’s answer? Why or why not?
cm
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. .
What is the length of the line?
First digit
Second digit
Last (estimated) digit is
5.?? cm
5.0? cm
5.00 cm
cm
Always estimate ONE place past the
smallest mark!
11.5 mL
So how many sig figs are there in
a given measurement?
52.8 mL
Be Wary of Wealth and Success!!
Charles Schwab, president of the largest steel company, died a
pauper.
Edward Hopson, president of the largest gas company, became
insane.
Richard Whitney, president of the New York Stock Exchange,
was released from prison to die at home.
Cosabee Rivermore, the Great Bear of Wall Street, died of
suicide.
Be Wary of Wealth and Success!!
Gene Sarazan, the U.S. Open and the PGA Golf Tournaments
Champion, went on to live a full and happy life playing golf
and remaining solvent.
Conclusion: Stop worrying about
business and start playing more
golf!!
How to Determine Significant
Figures in a Problem

Use the following rules:
Rule #1

Every nonzero digit is significant
Examples:
24 = 2
3.56 = 3
7
=1
Rule #2 – Sandwiched 0’s

Zeros between non-zeros are
significant
Examples:
7003 = 4
40.9 = 3
Rule #3 – Leading 0’s

Zeros appearing in front of non-zero
digits are not significant
• Act as placeholders
• Can’t be dropped, show magnitude
Examples:
0.00024 = 2
0.453
=3
Rule #4 – Trailing 0’s with DP

Zeros at the end of a number and to the right of
a decimal point are significant.
Examples:
43.00 = 4
1.010 = 4
1.50 = 3
Rule #5 – Trailing 0’s without DP

Zeros at the end of a number and to the left of a
decimal point aren’t significant
Examples:
300
= 1
27,300 = 3
Easier Way to do Sig Figs!!
• Pacific/Atlantic
P
A
If a decimal point is present, start on the Pacific (P)
side and draw an arrow through the number
until you hit a non-zero digit. Count all
numbers without an arrow through them.
If a decimal is absent, start on the Atlantic (A) side
and draw an arrow through the number until
you hit a non-zero digit.
Examples:
123.003 grams
decimal present, start on “P” side, draw
arrow, count digits without an arrow
through it.
Answer = 6
10,100 centimeters
Decimal absent, start on “A” side, draw an
arrow, count digits without an arrow
through it.
Answer = 3
Learning Check
State the number of significant figures in each
of the following:
A. 0.030 m
1
2
3
B. 4.050 L
2
3
4
C. 0.0008 g
1
2
4
D. 3.00 m
1
2
3
E. 2,080,000 bees
3
5
7
Learning Check
A. Which answer(s) contain 3 significant figures?
1) 0.4760
2) 0.00476
3) 4760
B. All the zeros are significant in
1) 0.00307
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
Learning Check
In which set(s) do both numbers contain the
same number of significant figures?
1) 22.0 m and 22.00 m
2) 400.0 m and 40 m
3) 0.000015 m and 150,000 m