Download Accuracy, Precision and Significant Figures

Our Objectives:
Be able to…
Accuracy, Precision
and
Significant Figures
Distinguish between
PRECISION and ACCURACY.
Determine the number of sig figs in a
measurement.
 Round any measurement to a set number of sig
figs.
 Use scientific notation when necessary.

Accuracy:



Precision:
This is the concept which deals with whether a
measurement is correct when compared to the
known value or standard for that particular
measurement.
When a statement about accuracy is made, it
often involves a statement about percent error.
error.
Percent error is often expressed by the following
equation:


This is the concept which addresses the degree of
exactness when expressing a particular measurement.
The precision of any single measurement that is made
by an observer is limited by how precise the tool
(measuring instrument) is in terms of its smallest unit.
Actual  Experiemental
% error 
Experimental
 100
Summary: Accuracy & Precision
Accuracy refers to how “correct” a measurement is; how
close it is to the accepted value.
Precision refers to how exactly a measurement is reported;
or how closely repeated measurements will agree.
A measurement can be precise, but inaccurate.
A measurement can be imprecise, but accurate.
Examples:
Balances
Kilogram bathroom scale.
Decigram balance.
Centigram balance.
Analytical balance.
1 METER BAR
Significant Figures
Significant Figures are ones that have been
accurately measured.
Sample Problems:
How many significant digits are in each of the following?
a. 903.2
b. 0.0090
c. 0.007
d. 0.02
e. 90.3
f. 0.090 0
g.
h.
i.
j.
k.
l.
0.0080
70
900.0
99
0.049
5.0002
1
Which Digits are
Significant Figures?

Rule 1: All non-zero numbers are significant.
Yep…More Practice Problems
1.
2.

Rule 2: All imbedded (flanked) zeroes are significant.

Rule 3: Leading zeroes are never significant.

Rule 4: Trailing zeroes are ONLY significant if there is
a decimal point present in the number.
3.
4.
5.
6.
7.
8.
9.
10.
Significant Figures:



When someone else has made a measurement,
you have no control over the choice of the
measuring tool or the degree of precision
associated with the device used.
You must rely on a set of rules to tell you the
degree of precision.
Refer to the “Tutorial: Significant Figures,
Precision, and Accuracy ” Handout (later)

No measurement is exact; there is always
some uncertainty.
There are always two parts to a
measurement:


Numerical part
Unit/label
5
3
3
3
4
4
2
2
3
3
What if I measured it?
You will be expected to use the rules for
significant figures…
figures…
in all your calculations…
calculations…
….and in all of your measurements
Measurements

3.0800
0.00418
7.09 x 10-5
91,600
0.003005
3.200 x10 9
250
780,000
0.0101
0.00800
Measuring with a Meter Stick




We know the object is greater than 2 and
less than 3.
We know the object is greater than 0.8
and less than 0.9
We can also guess at one more place. So,
I’ll guess 0.04
Final answer 2.84 cm.
2
Meter Stick Example 1

What length is indicated by the arrow?
•
•
•
•
Meter Stick Example 2

What length is indicated by the arrow?
More than 4, less than 5.
More than 0.5 but less than 0.6
Guess at 0.00
So, 4.50 cm.
9.40 cm
Measuring with a
Thermometer
Meter Stick Example 3

What length is indicated by the arrow?


12.34 cm


Thermometer Example 1

What is the
temperature?
28.5 °C
What is the
temperature?
Greater than 15, but
less than 16.
Guess one place. So,
0.0
Final answer = 15.0 °C
Thermometer Example 2

What is the
temperature?
21.8 °C
3
Measuring with a
Graduated Cylinder
Thermometer Example 3

What is the
temperature?



36.0 °C


Graduated Cylinder Example 1

What is the volume?
Graduated Cylinder Example 2

What is the volume?
27.5 mL
4.28 mL
Multiplication and Division with
Significant Figures
Graduated Cylinder Example 3

What is the volume?
Read to the bottom of
the meniscus.
Greater than 30, less
than 31.
Guess at one. So, 0.0
Answer 30.0 mL
What is the volume?

Rule: Your final answer cannot contain
any more significant figures than the least
precise measured number; the measured
number with the fewest significant figures.
5.00 mL
4
Significant Figures:
Multiplication and Division
Round to least amount of significant
figures
3.22 cm
X 2.1 cm
6.762 cm
The answer would then be 6.8cm

Adding and Subtracting with
Significant Figures


As always, the answer is never more
precise than the numbers used in the
math: you can never be more precise than
the least precise measurement.
In addition and subtraction, only look at
the decimal portion of the number.
Practice
1.
2.
3.
4.
5.
6.
8.6
2.5 x 3.42 =
14.0
3.10 x 4.520 =
3.0 x 10 1
2.33 x 6.085 x 2.1 =
114
(4.52 x 10-4) / (3.980 x 10-6) =
7
-4
6.17 x 10 10
(3.4617 x 10 ) / (5.61 x 10 ) =
(2.34 x 102)(0.012)(5.2345 x 105) = 1500000
Adding and Subtracting with
Significant Figures
Rules:
1.
Count the number of significant digits in the
decimal portion of each measured number.
2.
Round the answer to the LEAST number of
places in the decimal portion.
Ex.
24.686 m
2.343 m
+ 3.21_m_
30.239 m
The correct answer is 30.24 m
Practice
3.461728 + 14.91 + 0.980001 +
5.2631 =
24.61
2.
23.1 + 4.77 + 125.39 + 3.581=
156.8
3.
22.101 – 0.9307=
21.170
4.
0.04216 – 0.0004134 =
0.04175
5.
564321 – 264321=
300000
1.
Practice Problems
5
Our Goals: Be able to…
 Determine the number of sig figs in a
measurement.
 Round any measurement to a set number of sig
figs.
 Use scientific notation when necessary.
6