chapter 2: analyzing data mrs. faria. do now: hand in the measuring activity – front of the...
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CHAPTER 2: ANALYZING DATA
Mrs. Faria
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DO NOW:
Hand in the Measuring activity – front of
the room!!
Identify different quantities that can be
measured and their units of
measurement.
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ESSENTIAL QUESTIONS
What are the SI base units for time, length, mass,
amount of substance and temperature?
How does adding a prefix change a unit?
How are the derived units different for volume and
density?
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VOCABULARY
Base unit
Second
Meter
Kilogram
Kelvin
Derived unit
Liter
Density
Mass
Measurement
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WHAT IS A MEASUREMENT?Comparison between an unknown and a standard.
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SI & BASE UNITS Systeme Internationale d’Unites
(SI) –
An internationally agreed upon
system of measurements.
Base Units
Defined unit in a system of
measurement that is based on an
object or event in the physical world,
and is independent of other units.
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BASE UNITS Time – second Based on the frequency of radiation given off by a cesium-133 atom
Distance – Meter Distance light travels in a vacuum in 1/299,792,458th of a second.
Mass – kilogram Actual mass of 1 kilogram (see picture)
Temperature – Kelvin Zero Kelvin (absolute zero) refers to the point where there is virtually no particle motion or kinetic energy.
Two other commonly used scales; Fahrenheit and Celsius.
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SI PREFIXES
SI Prefixes are
multipliers that
precede the base
unit.
You must know
the three that are
outlined.
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DERIVED UNITS
Not all quantities can be measured
with SI base units.
Derived Units – a unit that is defined
as a combination of base units.
Speed – The SI unit for speed is m/s
(measurement of distance divided by time)
Volume – SI unit for volume is cm3.
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VOLUME
1 mL – volume of liquid that
occupies a 1cm x 1cm x 1cm cube
1 mL = 1 cm3
QUESTION – How many mL in a
1m x 1m x 1m (1m3) box?
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DENSITY
Density – derived unit that describes the amount of mass per unit of volume. g/cm3
g/mL Kg/L
𝐷𝑒𝑛𝑠𝑖𝑡𝑦=𝑚𝑎𝑠𝑠𝑣𝑜𝑙𝑢𝑚𝑒
𝐷=𝑚𝑉
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DENSITY SAMPLE PROBLEM Problem When a piece of aluminum is placed in a 25-mL graduated cylinder that contains 10.5 mL of water, the water level rises to 13.5 mL. What is the mass of the aluminum? (density of aluminum is 2.7 g/mL).
GIVEN (variable, number, units)
V = 3 mL
D = 2.7 g/mL
UNKNOWN (variable, question mark, units)
m = ? g
FORMULA (no need
to rearrange formula)
SUBSTITUTION (Substitute in numbers with units)
SOLUTION (Variable, number, units)
m = 8.1 g
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SAMPLE PROBLEM #2
Question 116 g of sunflower oil is used in a recipe. The density of the oil is 0.925 g/mL. What is the volume of the sunflower oil in mL?
m = 116 g
V = ? mL
D = 0.925 g/mL
V = 125 mL
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DENSITY- PRACTICE PROBLEM 1 An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ? g
WORK:
V
MD
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DENSITY – PRACTICE PROBLEM 1 SOLUTION An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ? g
WORK:M = DV
M = (13.6 g/cm3)(825cm3)
M = 11,200 gV
MD
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DENSITY – PRACTICE PROBLEM 2 A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mLV = ? mLM = 25 g
WORK:
V
MD
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DENSITY – PRACTICE PROBLEM 2 SOLUTION A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mLV = ? mLM = 25 g
WORK:V = M D
V = 25 g
0.87 g/mL
V = 29 mLV
MD
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SECTION 2: SCIENTIFIC NOTATION
& DIMENSIONAL ANALYSIS
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ESSENTIAL QUESTIONS & VOCABULARY Why use scientific notation to express numbers?
How is dimensional analysis used for unit conversions?
VOCABULARY
Scientific notation
Dimensional analysis
Conversion factor
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SCIENTIFIC NOTATION
Used to express any numbers as a number between 1 and 10 multiplied by 10 raised to a power.
5,450,000 5.45 x 106
Exponent
Coefficient
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SCIENTIFIC NOTATION
Converting into Sci. Notation:Move decimal until there’s 1 digit to its left. Places moved = exponent.
Large # (>1) positive exponentSmall # (<1) negative exponent
Only include sig figs.
65,000 kg 6.5 × 104 kg
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SCIENTIFIC NOTATION
Positive Power – number larger than 1
2.3 x 105 230,000
Negative power – number smaller than 1
2.3 x 10-5 0.000023
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SCIENTIFIC NOTATION – PRACTICE PROBLEMS
1) 2,400,000 g
2) 0.00256 kg
3)7 10-5 km
4)6.2 104 mm
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SCIENTIFIC NOTATION – PRACTICE SOLUTIONS
1) 2,400,000 g
2) 0.00256 kg
3)7 10-5 km
4)6.2 104 mm
2.4 106 g
2.56 10-3 kg
0.00007 km
62,000 mm
Convert the following to proper scientific notation
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SCIENTIFIC NOTATION – ADDITION & SUBTRACTION
In order to add or
subtract numbers
written in scientific
notation, the
exponents must be
the same!!!
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SCIENTIFIC NOTATION: MULTIPLICATIONMultiply the coefficients Use properties of exponents to multiply the power of 10 Simplify
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SCIENTIFIC NOTATION: DIVISION
Divide the coefficients.
Use properties of exponents to multiply the power of 10 Simplify
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SCIENTIFIC NOTATION- CALCULATIONS
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
5.44EXPEXP
EEEE÷÷
EXPEXP
EEEE ENTERENTER
EXEEXE7 8.1 4
= 671.6049383= 670 g/mol= 6.7 × 102 g/mol
Type on your calculator:
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DIMENSIONAL ANALYSISDimensional Analysis: systematic approach to
problem solving that uses conversion factors to move,
or convert from one unit to another.
Conversion Factor: ratio of equivalent values having
different units.
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DIMENSIONAL ANALYSIS: PRACTICE
360 s to ms
4800 g to kg
5600 dm to m
72 g to mg
2.45 x 102 ms to s
5 g/cm3 to kg/m3
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SECTION 3: UNCERTAINTY IN DATA
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ESSENTIAL QUESTIONS & VOCABULARY
How do accuracy and precision compare?
How can the accuracy of experimental data be described using error and percent error?
What are the rules for significant figures and how can they be used to express uncertainty in measured and calculated values?
VOCABULARYAccuracy Precision Error
Percent Error Significant Figure
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BAKING COOKIESWhat are some of the measurements required in making cookies?
Cup, tablespoon, Teaspoon.
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BAKING COOKIESWould a batch of cookies turn out ok if all ingredients would be measured in teaspoons?
NO!!! = too much error would build up.
It is important to select appropriate measurement instruments based on
the amounts needed!!!!
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ACCURACY VS. PRECISION
Accuracy - how close a measurement is to the accepted value
Precision - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
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PERCENT ERROR
Indicates accuracy of a measurement
100literature
literaturealexperimenterror %
your value
accepted value
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PERCENT ERROR - EXAMPLE
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
100g/mL 1.36
g/mL 1.36g/mL 1.40error %
% error = 2.90 %
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SIGNIFICANT FIGURES
Indicate precision of a measurement.
Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit
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SIGNIFICANT FIGURES
Indicate precision of a measurement.
Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit
2.35 cm
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SIGNIFICANT FIGURES
Count all numbers EXCEPT:Leading zeros -- 0.0025
Trailing zeros without a decimal point -- 2,500
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4. 0.080
3. 5,280
2. 402
1. 23.50
SIGNIFICANT FIGURESCounting Sig Fig
Examples1. 23.50
2. 402
3. 5,280
4. 0.080
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4. 0.080
3. 5,280
2. 402
1. 23.50
SIGNIFICANT FIGURESCounting Sig Fig
Examples1. 23.50
2. 402
3. 5,280
4. 0.080
4 sig figs
3 sig figs
3 sig figs
2 sig figs
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SIGNIFICANT FIGURES Calculating with Sig FigsMultiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
324 g
4 SF 3 SF3 SF
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SIGNIFICANT FIGURES
Calculating with Sig Figs (con’t)Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.
3.75 mL+ 4.1 mL 7.85 mL
224 g+ 130 g 354 g 7.9 mL 350 g
3.75 mL+ 4.1 mL 7.85 mL
224 g+ 130 g 354 g
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SIGNIFICANT FIGURES
Calculating with Sig Figs (con’t)Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm“1” in any conversion: 1 in = 2.54 cm
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SIGNIFICANT FIGURES: PRACTICE PROBLEMS5. (15.30 g) ÷ (6.4 mL)
= 2.390625 g/mL
18.1 g
6. 18.9 g- 0.84 g18.06 g
4 SF 2 SF
2.4 g/mL2 SF
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Determine the number of significant figures in the following: 8,200, 723.0, and 0.01.
A. 4, 4, and 3
B. 4, 3, and 3
C. 2, 3, and 1
D. 2, 4, and 1
PRACTICE QUESTION
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A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error?
A. 0.10 %
B. 0.20 %
C. 10 %
D. 20 %
PERCENT ERROR: PRACTICE QUESTION
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SECTION 4: REPRESENTING DATA
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ESSENTIAL QUESTIONS & VOCABULARYWhy are graphs created?
How can graphs be interpreted?
VOCABULARY
Graph
Interpolation
Extrapolation
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GRAPHING A graph is a visual display of data that makes trends easier to see than in a table.
A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.
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GRAPHING – BAR GRAPHS Bar graphs are often used to show how a quantity varies across categories.
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GRAPHING – DEPENDENT & INDEPENDENT VARIABLESOn line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.
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GRAPHING – FINDING THE SLOPE If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.
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INTERPRETING GRAPHSInterpolation is reading and estimating values falling between points on the graph.
Extrapolation is estimating values outside the points by extending the line.
This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods.