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### Data Analysis Chapter 2 Units of Measurement Is a measurement useful without a unit? SI Units The metric system is used worldwide. Long ago, inexact measurements were ... – PowerPoint PPT presentation

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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)

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
• 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.

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
• 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
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
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.