Transcript MT.4 – Accuracy, Precision, Sig Figs and Scientific Notation Methods…Game of Darts!, Hand outs 1) SLIDES 3 – 12 Make Handout (4 or.

MT.4 – Accuracy, Precision, Sig Figs and Scientific Notation
Methods…Game of Darts!, Hand outs
1)
SLIDES 3 – 12 Make Handout (4 or 6 per page)
2)
Setup dart boards – Middle – put a red bullseye and one black circle around it. STUDENT A, STUDENT B ON TOP
1)
Darts, ceiling tiles – 2, bulls eye printout
2)
Hide Bulls eye on STUDENT A’s board under another sheet of green paper
3)
Show Slide 1 – Definition of accurate and precise
4)
Pick a great dart player and one horrible dart player – both through three darts until one is precise and accurate and
the other is inaccurate and imprecise. Pull out accurate and precise examples.
5)
Uncover the bulls eye on accurate and precise board and say that the ACTUAL bulls eye was down here.
Therefore although Student A was very precise they were inaccurate.
6)
Assign Questions as Self Check
7)
Sig Figs and Sci Notation Quiz
MT.5 – Graphing
1)
2)
3)
4)
5)
Methods…Slides with Interactive Graphing and Handout
SLIDES
Package includes slides 13 – 18 and 20-23 followed by the two graphing exercises and a piece of graph paper
Graph interactively with the students.
Assign graphs as self check
Graphing Quiz
Accuracy
• the closeness of a set of
measurements to the CORRECT or
ACTUAL value
Precision
• the closeness of a set of measurements
Physics
Chemistry
Accuracy and Precision in Physics
Four students measure the velocity of a car using a radar gun. Their results are
below. The fifth student was in the car and the ACTUAL speed was 124.3 m/s.
Student A
Student B
Student C
Student D
Trial 1
121.0 m/s
100.5 m/s
124.0 m/s
90.2 m/s
Trial 2
121.3 m/s
121.5 m/s
123.9 m/s
122.1 m/s
Trial 3
121.1 m/s
150.5 m/s
124.8 m/s
72.2 m/s
Average
121.1 m/s
124.2 m/s
124.2 m/s
94.8 m/s
Make a statement about student A’s precision:
Make a statement about student A’s accuracy:
a)
when compared to student B
a)
when compared to student B
b)
when compared to student C
b)
when compared to student C
c)
when compared to student D
c)
when compared to student D
Accuracy and Precision in Chemistry
Four students measure the mass of a sample of Tungsten using a scale. Their
results are below. The teacher preweighed the sample on a more accurate scale at
least ten times and the ACTUAL mass was 124.3 g.
Student A
Student B
Student C
Student D
Trial 1
121.0 g
100.5 g
124.0 g
90.2 g
Trial 2
121.3 g
121.5 g
123.9 g
122.1 g
Trial 3
121.1 g
150.5 g
124.8 g
72.2 g
Average
121.1 g
124.2 g
124.2 g
94.8 g
Make a statement about student A’s precision:
Make a statement about student A’s accuracy:
a)
when compared to student B
a)
when compared to student B
b)
when compared to student C
b)
when compared to student C
c)
when compared to student D
c)
when compared to student D
Percent Error 
Actual Experimental
Actual
100
Calculate the %Error for Student A and Student B
Significant Figures
The number of significant figures is a result of the limits in the uncertainty of our
measurement tool. On your ruler you can probably estimate down to 0.5 mm if you
have mm divisions. So when asked to measure something that is between 4 and 5
millimeters long you can use 2 significant figures – 4.5 mm.
What is the difference between 100 Kg and 110 Kg in terms of precision?
Multiplication and division with significant figures
•we can only use as many as the given quantity with the FEWEST significant
figures.
•Example:
Significant Figures Continued
Addition and subtraction with significant figures
•When measurements are added or subtracted, the answer can contain no
more decimal places than the least precise measurement.
•Example
CONVERSION FACTORS and THINGS WE COUNT with whole numbers tend
to have infinite significant figures and do NOT limit the number of significant figures
in our answer.
Examples:
1000 m = 1 Km has infinite sig figs.
12 eggs = 1 dozen has infinite sig figs.
Rules for Significant Figures
1)
Zeros appearing between nonzero digits are significant.
2)
Zeros appearing in front of all nonzero digits are not significant.
3)
Zeros at the end of a number and to the right of a decimal point
are significant.
4)
Zeros at the end of a number without a decimal point are
insignificant. Zeros at the end of a number with a decimal point
are significant.
Examples
0.0009 kg
40.7 L
0.095 897 m
2000 m
2000. m
9.000 000 000 mm
8.50 x 105 g
87 009 km
Number of Sig
Figs
Rule
Scientific Notation
•
•
Proper scientific notation has 1 NON-ZERO digit before the decimal  3.3 x 104 cm
Units are placed AFTER the ‘x 104’
Which are in proper scientific notation? 33.04 x 104 cm .301 x 104 cm 2.500 x 104 cm
Why and when to use it?
1)
When tired of writing out very large or small numbers
Example: 3.12 x 1015 cm = 3,120,000,000,000,000 cm
2)
When wanting to show a certain number of significant figures
Example: 700,000 cm with 3 significant figures is 7.00 x 105 cm
Means:
600,000 cm to 800,000 cm
Means: 699,000 cm to 701,000 cm (more precise)
Entering 3.00 x 10-8 on a calculator: 3.00 EXP +/-
8
NOT 3.00 X 10
yX
EE
And here is why…
3.2 x 108 * 9.8 x 10-3
1.1 x 104
Stand up and sit down when you get
the correct answer (285.09), not the
wrong answer (2.85 x 1010)
+/-
8
Scientific Notation Practice
Scientific
Notation
Significant
Figures
Expanded Form
(Standard Form)
0.000203 Kg
2.304 x 10-3 m/s
102,000 g
5.40 x 105 J
987.22 cm
4.00 x 10-4 g
3m
Percent Error, Sig Figs and Scientific Notation Practice
Chemistry
Physics
Pg 60
Pg 27 15, 16
Pg 28 17-20
Pg 20 1, 2, 3
Pg 22 6, 8
Pg 23 9, 10, 11
35, 36, 38-42, 4345, 48, 49, 50, 54,
58
Answers in the
answer binder
Answers in the text
Graphing
Terminology
- Independent variable (Manipulated variable or the cause)
- Dependent variable (Responding variable or the effect)
Example – if we decrease the concentration of oxygen in the room then the exam scores
will be lower. Circle the INDEPENDENT variable.
Graphing Tips
1)
2)
3)
4)
5)
6)
Title, Name, Date
Put the dependent on the Y axis
Choose a domain and range such that your data points JUST barely fit on the page
Label your axis and include units
Plot your data
Draw a ‘best fit’ line or curve
1) This represents a mathematical AVERAGE
2) It doesn’t have to go through ALL dots – IT IS NOT CONNECT THE DOTS
3) Watch for OUTLIERS – data which doesn’t fit due to experimental error
1)
Perform a mathematical analysis if it is linear ( y = mx + b, m = rise/run)
Graphing – Tells us a relationship amongst variables
Types of Graphs – according to Mr. Riffel, the textbook and the Math department.
1)
2)
Directly proportional
1) Always linear
2) y α x reads as y is proportional to x
3) Formally in order to be directly proportional, y = x • c OR y / x = c
Where c is a constant number.
V=d/t
Examples:
At constant speed (V), distance is
y  4x
y  4 x
directly proportional to the time
taken:
1 hour = 60 miles
Inversely proportional
2 hours = 120 miles
1)
2)
3)
Produces curves (hyperbolas)
y α 1 / x reads as y is proportional to 1/x OR y is inversely proportional to x
y = 1 / x • c OR y • x = c
Examples:
1
f 
T
3) There are other types of graphs in science and mathematics such as parabolic, quadratic
and logarithmic graphs which are unique in their own ways. We will not concern
ourselves with them at this point.
y = 4x
x
1
2
3
4
5
6
7
8
y
4
8
12
16
20
24
28
32
0
2
Direct Check
Inverse Check
y/x=c
4
4
4
4
4
4
4
4
y*x=c
4
16
36
64
100
144
196
256
35
30
25
20
15
10
5
0
4
6
8
10
y = -4x
x
1
2
3
4
5
6
7
8
y
-4
-8
-12
-16
-20
-24
-28
-32
0
2
Direct Check
Inverse Check
y/x=c
-4
-4
-4
-4
-4
-4
-4
-4
y*x=c
-4
-16
-36
-64
-100
-144
-196
-256
0
4
6
8
10
-5
-10
-15
-20
-25
-30
-35
Just because it points downward
doesn’t mean it is inverse!
f=1/T
T (our x)
1
2
3
4
5
6
7
8
f (our y)
1
0.5
0.333333333
0.25
0.2
0.166666667
0.142857143
0.125
Direct Check
Inverse Check
y/x=c
1
0.25
0.111111111
0.0625
0.04
0.027777778
0.020408163
0.015625
y*x=c
1
1
1
1
1
1
1
1
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
Classify each of the graphs as directly or inversely proportional
Draw a best fit line/curve and classify the type of graph
Classify each of the graphs as directly or inversely proportional
Inversely
Directly
Proportional Proportional
Directly
Inversely
Inversely
Proportional Proportional Proportional
Draw a best fit line/curve and classify the type of graph
Inversely
Random – No
Directly
Inversely
Directly
Proportional Proportional Relationship Proportional Proportional
Mass vs. Volume of Aluminum
(Directly Proportional - Y / X is a constant - Linear)
45
Mass (g)
54.4
65.7
83.5
97.2
105.7
86
40
Volume (cm3)
35
30
Volume (cm3)
20.1
24.15
30.9
35.8
39.1
36
25
Vm
20
15
10
5
0
0
20
40
60
80
100
120
Mass (g)
We need to finish this graph: Best fit line or curve, mathematical analysis
140
Predictions from graphs
Given X can we predict what Y might be? Yes – two ways.
1) Interpolation
•
•
•
the X that is given is within the original data points.
quite a reliable prediction
example: Interpolate the volume of 75g of Aluminum in the
previous graph.
2) Extrapolation
•
•
•
•
The X that is given is OUTSIDE the original data points.
We must EXTEND our best fit line to reach X and predict Y
Less reliable prediction
Example: Extrapolate the volume of 20g of Aluminum in the
previous graph.
Volume vs Pressure of Nitrogen
(Inversely Proportional - x * y is a constant)
600
Pressure (kPa)
100
150
200
250
300
350
400
450
Volume (cm3)
500
400
Volume (cm3)
500
333
250
200
166
143
125
110
P*V
50000
49950
50000
50000
49800
50050
50000
49500
300
1
V
P
200
100
0
0
100
200
300
400
Pressure (kPa)
We need to finish this graph: Best fit line or curve, NO MATH ANALYSIS
500
Mass vs. Volume of Aluminum - Student B
(Directly Proportional - Y / X is a constant - Linear)
45
40
Volume (cm3)
35
30
25
Mass (g)
Volume
(cm3)
54.4
18
65.7
25.8
83.5
30.5
97.2
37.1
105.7
42.6
86
36
20
Vm
15
10
5
0
0
20
40
60
80
100
120
Mass (g)
We need to finish this graph: Best fit line or curve, mathematical analysis
140