Transcript Accuracy & Precision

BELLWORK 9/2/15

How does a scientist reduce the frequency of
human error and minimize a lack of accuracy?
A.
 B.
 C.
 D.

Take repeated measurements
Use the same method of measurement
Maintain instruments in good working order.
All of the above
Why do we have to learn
about Sig Figs?

Sig Figs tell you what place to round your
answers to.
Your final measurement (answer) can never be
more precise than your starting measurement.
 To understand that idea, we will discuss
accuracy vs. precision

Accuracy & Precision
Two important points in measurement
THE BIG CONCEPT
1. Accuracy –indicates the closeness of the
measurements to the true or accepted value.
Beware of Parallax – the apparent shift in
position when viewed at a different angle.
2. Precision - The closeness of the results to
others obtained in exactly the same way.
Accuracy vs. Precision
High Accuracy
High Precision
High Precision
Low Accuracy
Master Archers
Can you hit the bull's-eye?
Three
targets with
three
arrows each
to shoot.
How do
they
compare?
Accurate
and
precise
Precise
but not
accurate
Neither
accurate
nor
precise
Can you define accuracy vs. precision?
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
Example - Precision

Which set is more precise?
A. 18.2 , 18.4 , 18.3
B. 17.9 , 18.3 , 18.8
C. 16.8 , 17.2 , 19.4
Recording Measurements




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.
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
Always estimate ONE place past the
smallest mark!
11.50mL
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
Precision and Instruments

Do all measuring devices have the same amount
of precision?
You indicate the precision of the
equipment by recording its
Uncertainty

Ex: The scale on the left has an
uncertainty of (+/- .1g)

Ex: The scale on the right has an
uncertainty of (+/- .01g)
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.
Significant Figures
In Measurements
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 to Determine Significant
Figures in a Problem

Use the following rules:
Rule #1

Every nonzero digit is significant
Examples:
24m = 2
3.56m = 3
7m
=1
Rule #2 – Sandwiched 0’s

Zeros between non-zeros are
significant
Examples:
7003m = 4
40.9m = 3
Rule #3 – Leading 0’s

Zeros appearing in front of non-zero
digits are not significant
• Act as placeholders
Examples:
0. 24m = 2
0.453m
= 3
Rule #4 – Trailing 0’s with
Decimal Points

Zeros at the end of a number and to the right of
a decimal point are significant.
Examples:
43.00m = 4
1.010m = 4
1.50m = 3
Performing Calculations
with Significant Figures
 Rule:
When adding or subtracting
measured numbers, the answer can
have no more places after the
decimal than the LEAST of the
measured numbers.
 Only count the Sig Figs that come
after the decimal.
Adding and Subtracting
 2.45cm
+ 1.2cm = 3.65cm,
Round off to  3.7cm
 7.432cm
+ 2cm = 9.432
Round to  9.4cm
Multiplication and Division
 Rule:
When multiplying or
dividing, the result can have no
more significant figures than the
least reliable measurement.
 Count all of the Sig figs in the
entire number.
Examples
56.78
2
cm
cm x 2.45cm = 139.111
Round to  139cm2
75.8cm
x 9.6cm = ?
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