Lab 2 Metric System Review, Data Analysis and...
Transcript of Lab 2 Metric System Review, Data Analysis and...
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Lab 2
Metric System Review, Data Analysis and Graphing
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Accuracy of Data and Decimal Numbers
The number of decimals reflects the accuracy of the data
Rounding of numbers (depends on data collected, type of
measurements, data presentation and equipment used)
A decimal to the right that > 5 raises the next decimal
A decimal to the right that < 5 has no effect on the next decimal
Don’t round off until the end of your calculation
Rounding and calculating: 3.7+2.6 = 4+3 = 7
Calculating and rounding: 3.7+2.6 = 6.3 = 6
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Rules for deciding the number of significant figures in a
measured quantity:
1) All nonzero digits are significant:
1234 g has ___ significant figures
1.234 g has ____ significant figures
1.2 g has ____ significant figures
2) Zeroes between nonzero digits are significant:
1002 kg has ____ significant figures
3.07 ml has ____ significant figures
3) Zeros left of the first nonzero digits (leading zeros) are not
significant:
0.001 oC has only ____ significant figure
0.012 g has ____ significant figures
Accuracy of Data and Significant Figures
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(4) Trailing zeros that are to the right of a decimal point in a
number are significant:
0.0230 mL has ____ significant figures
0.20 g has ____ significant figures
(5) When a number ends in zeros that are not to the right of a
decimal point, the zeros are not necessarily significant:
190 miles may be 2 or 3 significant figures
50,600 calories may be 3, 4, or 5 significant figures
Accuracy of Data and Significant Numbers
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The potential ambiguity in the last rule can be avoided by the use
"scientific notation”
N = (coefficient x10e)*
50,600 calories as:
5.06 × 104 calories (3 significant figures)
5.060 × 104 calories (4 significant figures)
5.0600 × 104 calories (5 significant figures)
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In addition and subtraction, the result is rounded off so that
it has the same number of digits as the measurement having
the fewest decimal places
For example, 100.2 + 23.643 = 123.843, which should be
rounded to ____
In multiplication and division, the result should be rounded
off so as to have the same number of significant figures as in
the component with the least number of significant figures
For example, 3.0 (2 significant figures ) × 12.60 (4
significant figures) = 37.800 which should be rounded to ___
The accuracy of a calculated result is limited by the least accurate
measurement involved in the calculation
Accuracy of Data and Significant Numbers
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Determine the number of significant figures in the following
measurements:
1) 0.0009
2) 15,450.0
3) 6 × 103
4) 87.990
5) 30.42
Write the following numbers in scientific notation:
1) 3675.890
2) 0.005643
3) 76904
4) 0.0067890
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Metric System
o Decimal based system
o Base units:
grams (g)
liters (l)
meters (m)
moles (M)
o Prefixes used to change the base unit by factors of 10
Giga (G), mega (M), kilo (k), deci (d), centi (c), milli (m),
micro (μ) and nano (n)
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Prefix Symbol Exponent of 10
kilo k 103
Base Unit BU 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
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Prefix kilo Base
Unit
deci centi milli micro nano
Symbol k BU d c m μ n
Exponent
of 10
103 100 10-1 10-2 10-3 10-6 10-9
25 kg = ? cg 25 kg = 25kg x 105cg
1kg
35 nm = ?dm
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The World of the Micrometer (Micron)
10-6 meters
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The World of the Nanometer
10-9 meters
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Data Analysis
o Mean
o Median
o Mode
o Standard Deviation
o Correlations
o Linear Regression
o Graphing
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Consider the following date:
7.3 m, 5.2 m, 5.2 m, 4.8 m, 6.7 m, 8.1 m
Mean = average
Median = central value after numbers have been
arranged from lowest to highest or vice versa
Mode = most frequently occurring number in a set of
data
Data Analysis/ Looking at the center of the data
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Variance (σ2): measurement of the spread between
numbers in a data set/ average of the squared differences
from the mean
Standard Deviation (σ): dispersion of the data from the
mean/ square root of variance
Standard Error of the Mean (SEM): measure of how
precise is our estimate of the mean
Data Analysis/ Looking at how scattered and precise
the data is
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Standard Deviation for Normally Distributed Data
Measure of how far each observed value is from the mean
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small standard deviation/ indicator of the closeness of the data
points to the arithmetic mean
Large standard deviation/ indicator that the data values are
dispersed over a wide range
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Correlation: Relationship between two variables/ zero,
positive, negative
Data Analysis
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Linear regression/ prediction of the values of one
variable from the values of a second variable
The variable we are predicting is called the criterion
variable and is referred to as Y
The variable we are basing our predictions on is called
the predictor variable and is referred to as X
Best-fit line
Interpolation
Extrapolation
Data Analysis
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Use the entire graph paper
Choose a range for your X and Y axis scales so that your data will fill
the entire page
Don’t crowd axes to the edge of the page. Leave enough room
to show and label your scales for X and Y axes
Good Graphing Rules
Have a descriptive TITLE that tells the reader what they are
viewing
Plot the independent variable on the X axis
(Time is always plotted on the X axis)
Plot the dependent variable on the Y axis
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If appropriate, draw a line of best fit for each data set
(DO NOT USE POINT-TO-POINT TO DRAW A LINE)
If appropriate, add error bars
Show a LEGEND defining each symbol, line, and error bars
(SD or SEM)
Use different symbols for different data sets
Draw the symbols large enough to be easily viewed
Good Graphing Rules