DATA ANALYSIS
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Transcript DATA ANALYSIS
DATA ANALYSIS
Using the Metric System
Scientific Notation
Percent Error
Using Significant Figures
Accuracy and Precision
Graphing Techniques
Using the Metric System
A. Why do scientists use the metric system?
The metric system was developed in France in
1795 - used in all scientific work because it has
been recognized as the world wide system of
measurement since 1960.
SI system is from the French for Le Systeme
International d’Unites.
The metric system is used in all scientific work
because it is easy to use. The metric system is
based upon multiples of ten. Conversions are
made by simply moving the decimal point.
Base Units (Fundamental Units)
QUANTITY
NAME
SYMBOL
_______________________________________________
Length
meter
m
----------------------------------------------------------------------------Mass
kilogram
kg
------------------------------------------------------------------------------Amount of Substance mole
mol
------------------------------------------------------------------------------Time
second
s
_______________________________________________
Derived Units
Base Units – independent of other units
Derived Units – combination of base units
Examples
density g/L (grams per liter)
volume m x m x m = meters cubed
Velocity m/s (meters per second
Metric Units Used In This Class
QUANTITY
Length
NAME
meter
centimeter
millimeter
kilometer
SYMBOL
m
cm
mm
km
Mass
gram
kilogram
centigram
milligram
g
kg
cg
mg
Volume
liter (liquid)
milliliter (liquid)
cubic centimeter (solid)
L (l)
mL (ml)
cm3
Metric Units Used In This Class
Density
grams/milliliter (liquid)
grams/cubic centimeter (solid)
grams/liter (gas)
Time
g/mL
g/cm3
g/L
second
s
minute
min
hour
h
volume measurement for a liquid and a solid
( 1 mL = 1 cm3) These are equivalents.
Equalities You Need To Know
1 km = 1000 m
1 m = 100 cm
1 m = 1000 mm
1L = 1000 mL
1kg = 1000g
1 g = 100cg
1 g = 1000 mg
Making Unit Conversions
Make conversions by moving the decimal point to the
left or the right using:
“ king henry died unit drinking chocolate milk”
Examples
1. 10.0 cm = __________m
2. 34.5 mL = __________L
3. 28.7 mg = __________kg
SCIENTIFIC NOTATION
Scientific Notation: Easy way to express very large
or small numbers
A.0 x
10x
A – number with one non-zero digit before decimal
x -exponent- whole number that expresses the number
decimal places
if x is (-) then it is a smaller
if x is (+) than it is larger
PRACTICE
Convert to Normal
2.3 x 1023 m
3.4 x 10-5 cm
Convert to SN
3,400,000,
.0000000456
Multiplying
Calculating in Scientific notation
Multiplying
Multiple the numbers
Add the exponents
(2.0 x 104) (4.0 x 103) = 8.0 x 107
Dividing
divide the numbers
subtract the denominator exponent from the numerator
exponent
9.0 x 107
3.0 x 105
3.0 x 102
Add
Add or subtract
get the exponents of all # to be the same
calculate as stated
make sure the final answer is in correct scientific notation
form
7.0 x 10 4 +
7. 0 x 104
70,000
3.0 x 10 3 =
+ .3 x 104 = 7.3 x 104
+ 3,000 = 73000= 7.3 x104
subtract
7.0 x 10 4 - 3.0 x 10 3 =
7.0x 104 – .30 x 104 = 6.7 x 104
70,000 - 3 000 =67,000
PRACTICE
Add:
2.3 x 103 cm + 3.4 x 105 cm
Subtract:
2.3 x 103 cm - 3.4 x 105 cm
Multiply:
:
2.3 x 103 cm X 3.4 x 105 cm
Divide:
:
2.3 x 103 cm / 3.4 x 105 cm
Calculating Percent Error
% Error =accepted value–experimental value
X
accepted or actual value
Subtract -Divide then multiply by 100
100= %
Calculating Percent Error
EXAMPLE – A student determines the density of a piece
of wood to be .45g/cm. The actual value is .55g/cm.
What is the student’s percent error?
.55 - .45 X 100% = .10 =
.18 x 100% = 18%
.55
.55
The following lesson is
one lecture in a series of
Chemistry Programs
developed by
Professor Larry Byrd
Department of Chemistry
Western Kentucky University
Introduction
If someone asks you how many inches there are in
3 feet, you would quickly tell them that there are
36 inches.
Simple calculations, such as these, we are able to
do with little effort.
However, if we work with unfamiliar units, such
as converting grams into pounds, we might
multiply when we should have divided.
The fraction ( 4 x 5) / 5 can be simplified by dividing the
numerator (top of fraction) and the denominator (bottom
of fraction) by 5:
45 45
= 4
5
5
Likewise, the units in (ft x lb) / ft reduces to pounds (lb)
when the same units ( ft )are canceled:
ft lb ft lb
= lb
ft
ft
CONVERSION FACTOR
A CONVERSION FACTOR is a given Ratio-
Relationship between two values that can also be
written as TWO DIFFERENT FRACTIONS.
For example, 454 grams =1.00 pound, states that there
are
454 grams in 1.00 pound or that
1.00 pound is equal to 454 grams.
Ratio-Relationship
We can write this Ratio-Relationship as two
different CONVERSION-FACTOR-FRACTIONS:
454 grams
1.00 pound
or
as
1.00 pound
454 grams
These fractions may also be written in words as
454 grams per 1.00 pound or as
1.00 pound per 454 grams, respectively.
The "per" means to divide by.
Example
If we want to convert
2.00 pounds into
grams, we would:
first write down the given quantity (2.00 lbs)
pick a CONVERSION-FACTOR-FRACTION that when
the given quantities and fractions are multiplied, the units
of pounds on each will cancel out and leave only the
desired units, grams.
We will write the final set-up for the problem as follows:
454 grams
2.00 pounds
1.00 pound
= 908 grams
If we had used the other conversion-factor-fraction in
the problem:
1.00 pound
pounds 2
0.0044
=
2.00 pounds
grams
454 grams
We would know that the ABOVE problem was
set-up incorrectly since WE COULD NOT
CANCEL Out the units of pounds and the
answer with pounds / grams makes no sense.
Four-step
approach
When using the Factor-Label Method
it is helpful to follow a four-step approach
in solving problems:
1. What is question – How many sec in 56 min
2. What are the equalities- 1 min = 60 sec
3. Set up problem (bridges) 56 min 60 sec
4.
1 min
5. Solve the math problem -multiple everything on top
6. and bottom then divide 56 x 60 / 1
Using Significant Figures (Digits)
value determined by the instrument of
measurement plus one estimated digit
reflects the precision of an instrument
example – if an instrument gives a length value to
the tenth place – you would estimate the value to the
hundredths place
1. all non-zero # are Sig fig-
314g
3sf
12,452 ml
5sf
2. all # between non-zero # are sig fig
3. place holders are not sf
101m
3sf
6.01mol
3sf
36.000401s
8s
0.01kg
1sf
4. zeros to the right of a decimal are sig fig if
Preceded by non-zero
3.0000s
0.002m
5sf
1sf
13.0400m
6sf
5. Zero to right of non-zero w/o decimal point
600m
1sf
are not sig fig
600.m
3sf
600.0 m
4sf
600.00 m
5sf
RULES FOR USING SIGNIFICANT FIGURES
use the arrow rule to determine the number of
significant digits
decimal present all numbers to right of the first non
zero are significant (draw the arrow from left to
right)
----------> 463
3 sig. digits
----------> 125.78
5 sig. digits
---------->
.0000568
3 sig. digits
----------> 865 000 000.
9 sig. digits
RULES FOR USING SIGNIFICANT FIGURES
use the arrow rule to determine
the number of significant digits
decimal not present < -------- all
numbers to the left of the first non
zero are significant (draw arrow from
right to left)
246 000 <---------- 3 sig. digits
400 000 000 <---------- 1 sig. digit
Use appropriate rules for rounding
If the last digit before rounding is less than
5 it does not change
ex. 343.3 to 3 places 343
1.544 to 2 places 1.54
If the last digit before rounding is greater
than 5 – round up one
ex. 205.8 to 3 places 206
10.75 to 2 places 11
use fewest number of decimal places rule for
addition and subtraction
1)
24.05
123.770
0.46
10.2
_________
2)
3)
4)
5.6
237.52
88
28
- 21.4
- 4.76
8.75
7
______ _______ ______
Use least number of significant figures
rule for multiplication and division
1)
23.7 x 6.36
2) .00250 x 14
3) 750. / 25
4) 15.5 / .005
Reliability of Measurement
ACCURACY – how close a measured value is to the
accepted value
PRECISION – how close measurements are to one
another - if measurements are precise they show
little variation
* Precise measurements may not be accurate
Precision- refers to how close a series of
measurements are to one another; precise
measurements show little variation over a
series of trials but may not be accurate.
LESS THAN .1 IS PRECISE
Oscar performs an experiment to determine the
density of an unknown sample of metal. He
performs the experiment three times:
19.30g/ml
19.31g/ml
19.30g/ml
Certainty is +/- .01
Are his results precise?
Accuracy – refers to how close a measured value is to an
(theoretical) accepted value.
The metal sample was gold( which has a density of 19.32g/ml)
Certainty is +/- .01
Are his results accurate? Need to calculate percent error.
5% OR LESS IS ACCURATE
Oscar finds the volume of a box 2.00cm3 (ml)
It is really 3.00ml is it precise? Accurate? Percent error
Oscar finds the volume of a box 2.00cm3 (ml)
It is really 3.00ml is it precise?
To know if it is precise you need more trials
Accurate? Percent error
Actual - Experimental X
Actual
3-2
3
X 100 = 33.3%
100% =
Activity: basket and paper clip
1. Throw 3 paper clips at basket
2. Measure the distance from the basket to determine
accuracy and precision
Cm3= ml and dm3= l Liter
Graphing
graph – a visual representation of data that reveals
a pattern
Bar- comparison of different items that vary by one
factor
Circle – depicts parts of a whole
Line graph- depicts the intersection of data for 2
variables
Independent variable- factor you change
Dependent variable – the factor that is changed when
independent variable changes
Graphing
Creating a graph- must have the following
points
1.
2.
3.
4.
5.
6.
7.
Title graph
Independent variable – on the X axis – horizontalabscissa
Dependent variable – on Y axis – vertical- ordinate
Must label the axis and use units
Plot points
Scale – use the whole graph
Draw a best fit line- do not necessarily connect the
dots and it could be a curved line.
Interpreting a graph
Slope-
rise
Run
X2 –X1
relationship
Y2 –Y1
direct – a positive slope
inverse- a negative slope
equation for a line – y = mx + b
m-slope
b – y intercept
extrapolate-points outside the measured valuesdotted line
interpolate- points not plotted within the measured
values-dotted line
WORK ON GRAPHING EXERCISES
Graphical analysis – click and go
GRAPHING LAB
Creating a graph- must have the following points
1.Title graph
2. Independent variable –on the X axis–horizontal- abscissa
3. Dependent variable – on Y axis – vertical- ordinate
4. Must label the axis and use units
5. Plot points
6. Scale – use the whole graph
7. Draw a best fit line- do not necessarily connect the dots and it
could be a curved line.
GRAPHING
Interpreting a graph
Slope= rise
Run
X2 –X1
relationship
Y2 –Y1
direct relationship– a positive slope
Inverse relationship- a negative slope
equation for a line – y = mx + b
m-slope
b – y intercept
extrapolate-points outside the measured valuesdotted line
interpolate- points not plotted within the measured
values-dotted line
Bulldozer Lab