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Data Analysis

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Title: Data Analysis


1
Data Analysis
  • Chapter 2

2
Units of Measurement
  • Is a measurement useful without a unit?

3
SI Units
  • The metric system is used worldwide.
  • Long ago, inexact measurements were used. For
    example
  • Boundaries wouldve been marked off by walking
    counting the number of steps.
  • Time was measured with a sundial or an hourglass
    filled with sand.

4
SI Units
  • The metric system was adopted in 1795 by a group
    of French scientists.
  • In 1960, an international committee of scientists
    met to update the metric system. Called the SI
    system (Systeme Internationale dUnites)

5
Base Units
  • There are 7 base units in SI. A base unit is a
    defined unit in a system of measurement that is
    based on an object or event in the physical
    world.
  • The base unit for
  • Time is second electrical current is
  • Length is meter amount of sub is
  • Mass is kilogram luminosity is
  • Temp is
  • The prefixes used with SI units are (table 2-2)

6
Derived Units
  • A derived unit is a unit that is defined by a
    combination of base units.
  • Example speed is meters/second (m/s)
  • Get out your calculators!

7
Volume
  • Volume is the space occupied by an object.
  • 1 L 1 dm3 1 mL 1 cm3
  • You would use a graduated cylinder to measure the
    volume of a liquid in the lab.
  • You would measure length x width x height to find
    the volume of a regular solid.
  • How would you find the volume of an irregular
    solid?

8
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9
Density
  • Density of a ratio that compares the mass of an
    object to its volume
  • Dm/v
  • Ex 1 Calculate the density of a piece of aluminum
    that has the mass of 13.5g a volume of 5.0cm3.
    What is this substance?

10
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11
  • Ex 2 Suppose a sample of aluminum (Al) is placed
    in a graduated cylinder containing 10.5 mL of
    water rises to 13.5 mL. What is the mass of the
    aluminum sample? (Use the density from example 1)

12
Density
  • Density of a substance is a property that doesnt
    change, UNLESS altered by an outside substance.
  • Dwater at STP is 0.998 g/cm3
  • Dwater at 4C is 1.00 g/cm3
  • practice problems 1-3

13
  • If we know the Density dimensions of a cube,
    can we determine the mass of the cube?
  • If the Dair 0.00122 g/cm3, then what is the mass
    of air in this room?

14
Temperature
  • Temperature is the measure of how hot/cold an
    object is relative to other objects.
  • Scales of temperature
  • Celsius- derived by Anders Celsius used the
    point at which water freezes boils to establish
    his scale
  • Freezing point- 0 C
  • Boiling point- 100 C

15
Temperature
  • Kelvin (K)- derived by William Thomson, known as
    Lord Kelvin
  • Kelvin is the SI base unit of temperature
  • Conversion process of Celsius to Kelvin
  • Add 273
  • Conversion process of Kelvin to Celsius
  • Subtract 273
  • Ex.

16
  • Practice problems 4-6
  • 4. Convert 357C to Kelvin
  • 5. Convert -39C to Kelvin
  • 6. Convert 266 K to Celsius

17
Scientific Notation
  • Scientific notation- expresses a number as a
    number between 1 10 and then raised to a power,
    or exponent.
  • When a number is more than one, the exponent is
    positive.
  • If less than one, the exponent is negative.

18
Scientific Notation
  • How do we convert data into Sci. Not. ?
  • Move the decimal until you have a number between
    1 10.
  • The exponent in the number of times you moved the
    decimal.
  • Put unit with answer.

19
Scientific Notation
  • Practice problems 1-8
  • 700 m
  • 38 000 m
  • 4 500 000m
  • 685 000 000 000 m

20
  • 5. 0.0054 kg
  • 6. 0.000 006 87 kg
  • 7. 0.000 000 076 kg
  • 8. 0.000 000 000 8 kg

21
Calculations with Sci Not.
  • How do we add/subtract using Scientific Notation?
  • Make sure exponents are the same.
  • If the exponent is too large, decrease it move
    the decimal that many times to the right.
  • If the exponent is too small, increase it move
    the decimal that many places to the left.

22
Calculations with Sci Not.
  • Ex. What is 2.70 x 107 15.6 x 106?
  • practice problems 5-8

23
  • 1.26x104 kg 2.5x103 kg
  • 7.06x10-3 kg 1.2x10-4 kg
  • 4.39x105 kg 2.8x104 kg
  • 5.36x10-1 kg 7.40x10-2 kg

24
Calculations with Sci Not.
  • How do we multiply/divide using sci. not.?
  • Multiply/divide the factors(aka coefficients)
    first.
  • Multiplication
  • Add the exponents.
  • Division
  • Subtract the exponent of the denominator from the
    exponent of the numerator.

25
Calculations with Sci Not.
  • Ex.1 What is (2 x 103) x (3 x 102)
  • Ex. 2 What is (9 x 108) / (3 x 10-4)
  • practice problems 9-16.

26
  • 9. (4x102 cm)x(1x108 cm)
  • 10. (2x10-4 cm)x(3x102 cm)
  • 11. (3x101 cm)x(3x10-2 cm)
  • 12. (1x103 cm)x(5x10-1 cm)
  • 13. (6x102 g)/(2x101 cm3)
  • 14. (8x104 g)/( 4x101 cm3)
  • 15. (9x105 g)/ (3x10-1 cm3)
  • 16. (4x10-3 g)/(2x10-2 cm3)

27
Dimensional Analysis
  • Dimensional analysis- method of problem-solving
    that focuses on the units used to describe
    matter often uses conversion factors.
  • Conversion factor- ratio of equivalent values
    used to express the same quantity in different
    units.
  • Ex 1 How many hours are in one year?

28
Conversion Factors
  • Giga
  • Mega
  • Kilo
  • Hecto
  • Deca
  • BASE
  • Deci
  • Centi
  • Milli
  • Micro
  • Nano
  • (Angstro)
  • Pico

29
Dimensional Analysis
  • Ex. 1 How many meters are in 48 km?
  • Practice
  • What conversion factor should be used for the
    following conversion?
  • A. 360 s ? ms
  • B. 4800 g ? kg
  • C. 6800 cm ? m

30
Practice using dimensional analysis
  • 4.5 L __________mL
  • 0.095mg ____________cg
  • 9500 mm ___________m
  • 0.575 km ___________m
  • 100 cm ___________mm

31
  • Handout Unit Conversion

32
Conversion
  • Ex. 2 What is the speed of 550 meters per second
    in kilometers per minute?

33
Practice
  • 6) How many seconds are there in 24.0 hours?
  • 86,400 s
  • 7) the density of gold is 19.3 g/mL. What is
    golds density in decigrams per liter?
  • 193,000dg/L
  • 8) A car is travelling 90. kilometers per hour.
    What is the speed in miles per minute? (1 km0.62
    mi)
  • 0.93 mi/min

34
Reliability
  • How reliable are measurements?
  • Accuracy Precision
  • Accuracy- refers to how close a measured value is
    to an accepted value.
  • Precision- refers to how close a series of
    measurements are to one another.

35
Accuracy or precision
36
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37
Percent Error
  • Percent error- ratio of an error to an accepted
    value.
  • error accepted(book value) exp (you) x
    100 accepted
  • error (error/accepted) x 100
  • Ignore the negative sign, only the amount of
    error matters.

38
Percent Error
  • Ex. You calculated the length of a steel pipe to
    be 5.2 m. The accepted length is 5.5 m. What is
    the percent error?

39
  • Practice 1
  • The accepted density for Cu is 8.96 g/mL.
    Calculate the percent error for the measurement
    8.86 g/mL.
  • Worksheet

40
Significant Figures
  • Significant figures- include all known digits
    plus one estimated digit.
  • Rules
  • Non-zero numbers are always significant
  • Ex. 72.3 Ex. 700
  • Sandwich zeros are significant.
  • 60.5
  • 809
  • 30.07

41
Significant Figures
  • 3. Final zeros after the decimal are significant.
  • a) 6.20
  • b) 9.00
  • c) 92.0
  • d) 0.009200
  • 4. Place holding zeros are not significant.
  • e) 0.095
  • f) 300
  • g) 50
  • h) 30,000

42
Significant Figures
  • You can convert to scientific notation to remove
    place holders.
  • 30,000 3 x 104
  • Example Determine the number of sig figs in the
    following masses.
  • a) 0.000 402 30 g
  • b) 405 000 kg
  • c) 8.20 x 107
  • practice problems p39 31 32

43
Rounding Off Numbers
  • Rounding to 3 sig figs
  • 2.5320? if the 4th sig fig is lt5, do not change
    the 3rd sig fig.
  • 2.5360? if the 4th sig fig is gt5, then round the
    3rd sig fig up.
  • Examples
  • 55.845 ?(4 sf)
  • 32.065 ?(2 sf)
  • 87.62 ?(1 sf)
  • 36,549,555 ?(2 sf)

44
Addition/subtraction with sig figs
  • Your answer must have the same number of digits
    to the right of the decimal as the measurement
    with the FEWEST digits to the right of the
    decimal.
  • Ex. Add the following measurements 28.0 cm,
    23.538 cm, 25.68 cm.

45
  • practice problems

46
Multiplication/division w/ sig figs
  • Your answer must have the same number of sig figs
    as the measurement with the fewest sig figs.
  • Ex. Calculate the volume of a rectangular object
    w/ the following dimensions length 3.65 cm,
  • width 3.2cm,
  • height 2.05 cm.

47
Multiplication/division w/ sig figs
  • practice problems 7-14
  • Check old worksheets
  • worksheet

48
Representing Data
  • Graph- visual display of data
  • Circle graph- usually used to represent
    percentages of something.

49
Representing Data
  • Bar graph- often used to show how a quantity
    varies with factors such as time, location, or
    temperature.
  • Independent variable- located on the x-axis
  • Dependent variable- located on the y-axis

50
Bar Graph
51
Representing Data
  • Line Graph- most often used in chemistry
  • The points on a line graph represent the
    intersection of data for 2 variables.
  • Independent variable- located on the x-axis.
  • Dependent variable- located on the y-axis

52
  • Best fit line- line drawn so that as many points
    fall above the line as fall below it.
  • Straight best fit- there is a linear relationship
  • The variables are directly related
  • Curved best fit- there is a nonlinear
    relationship.
  • The variables are inversely related

53
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54
Interpreting Data
  • First thing, ID the variables independent
    dependent
  • Notice what measurements were taken
  • Decide if the relationship of the variables is
    linear/nonlinear.
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