The Metric System Scientific Notation Significant Figures Measuring Techniques Metric Conversion Gra - PowerPoint PPT Presentation

Loading...

PPT – The Metric System Scientific Notation Significant Figures Measuring Techniques Metric Conversion Gra PowerPoint presentation | free to view - id: 25105-MjY1Z



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

The Metric System Scientific Notation Significant Figures Measuring Techniques Metric Conversion Gra

Description:

Metric Conversion. Graphing Techniques. Algebra Skills. A Physics ToolKit. The Metric System ... Metric Conversions. 52. Conversion of Units ... – PowerPoint PPT presentation

Number of Views:2967
Avg rating:5.0/5.0
Slides: 77
Provided by: HPS
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: The Metric System Scientific Notation Significant Figures Measuring Techniques Metric Conversion Gra


1
The Metric SystemScientific NotationSignificant
FiguresMeasuring Techniques Metric
ConversionGraphing TechniquesAlgebra Skills
A Physics ToolKit
2
The Metric System
3
The Metric System
  • Developed in France in the 1790s.
  • Is widely used in all but three countries.
  • Has been adopted in the scientific community.
  • Missed being nationalized in the US in early
    1800s by one vote.

4
Advantages
  • Based on the decimal system. (powers of ten)
  • Because it is used almost world wide it makes
    commercial trade easier.

5
Some Prefixes
6
Mass
  • Amount of material in an object.
  • Metric units grams, kilograms
  • Special Note Mass is different than weight.
    Weight is the response of mass to the pull of
    gravity.

7
Volume
  • Volume is the amount of space that an object
    takes up.
  • Metric units mL, L, or cm3, m3

8
Length
  • Metric Units cm, m, km
  • English Units inches, yards, miles
  • FYI 1 mile 1.6 km

9
Scientific Notation
10
Scientific Notation
  • Physics deals with very large and small numbers
    and Scientific Notation makes it easier to
    express these numbers.
  • 0.00000000000000000000663
  • 6.63 x 10-24

11
Format for Scientific Notation
  • 1. The first number will always be between 1 and
    10.
  • 2. The last part will always be 10 raised to some
    power.
  • 3. The two parts are separated by x.

12
How to do it
  • Locate the decimal point and move it so there is
    one leading digit.
  • 29,190,000,000 becomes 2.919
  • Now count how many places you moved the decimal
    point and place it in the exponent position. (If
    you moved left the exponent is positive.
  • 2.919 x 1010

13
Another example
  • Change 0.00000000259 into sci.not.
  • First, move the decimal
  • 2.59
  • Then count how many places you moved the decimal
    and record it in the exponent position. (Moving
    right? go neg.)
  • 2.59 x 10 -9

14
Looks goodBut Not Really
  • Is this number in correct sci.not.?
  • 428.5 x 109Nope.
  • You fix it the same as before.
  • Move the decimal
  • 4.285
  • Then fix the exponent. Since you moved the
    decimal to the left 2 raise the power 2.
  • 4.285 x 1011

15
One more for the road.
  • 0.0234 x 105 Look good???
  • Nope. Well, fix it then.
  • Yep, the decimal
  • 2.34
  • Then the power.
  • 2.34 x 10 3
  • Notice the the decimal moved right and the
    exponent was decreases the same amount.

16
Practice Makes Perfect
  • 28,000,000
  • 305,000
  • 0.00000463
  • 0.0034
  • 2101 x 105
  • 0.0029 x 10-32
  • 2.8 x 107
  • 3.05 x 105
  • 4.63 x 10-6
  • 3.4 x 10-3
  • 2.101 x 108
  • 2.9 x 10-35

17
Adding and Subtracting Numbers in Scientific
Notation
  • Treat the number as two parts separated by the
    x.
  • BIG RULE The exponent needs to be the same.
  • Ex) 1.5 x 102 2.3 x 102 3.8 x 102
  • You add the first part like you normally would
    and then add the x 10 the exponent remains the
    same.

18
nother example
  • 4.5 x 103 2.0 x 102 ??
  • Whoops, cant add yet. You need to make the
    exponents the same.
  • Change 2.0 x 102 into 0.2 x 103 .
  • So, 4.5 x 103 0.2 x 103 4.7 x 103
  • Subtraction works the same way

19
Some Practice
  • 2.3 x 102 4.5 x 102
  • 1.3 x 103 4.5 x 102
  • 5.9 x 109 - 3.2 x 108
  • 2.30 x 104 - 4.50 x 102
  • 6.8 x 102
  • 1.8 x 103 (rounded)
  • 5.6 x 109 (rounded)
  • 2.26 x 104

20
Multiplication and Division with Scientific
Notation
  • This is actually easier than adding and
    subtracting because the exponents do not need to
    be the same.
  • Multiplication Rule Multiply the first part and
    add the exponents.
  • Ex) (2.0 x 102)(3.5 x 103) 7.0 x 105

21
continued
  • Division Rule Divide the first part and subtract
    the exponents.
  • Ex) (5.0 x 107) / (2.0 x 103) 2.5 x 104

22
Some Practice
  • (2.32 x 107)x(2.0 x 103) ???
  • (4.5 x 105)x(4.0 x 10-2) ???
  • (1.5 x 10-2)x(3.0 x 10-2) ???
  • (4.5 x 105)/(1.5 x 102) ???
  • (9.0 x 108)/(3.0 x 10-3) ???
  • (6.8 x 10-5)/(2.0 x 10-2) ???

4.64 x 1010 18 x 103 or 1.8 x 104 4.5 x
10-4 3.0 x 103 3.0 x 1011 3.4 x 10-3
23
Significant Figures
24
Significant Figures
  • Whats the reason for using significant figures?
  • You can only report a number as accurate as the
    instrument. Not all numbers are important.
  • Our meter sticks will not measure out to a degree
    of accuracy like 1.000056789 m.

25
Significant Figures
  • Three Rules
  • Non-zero digits are always significant.
  • Any zeros between two significant digits are
    significant.
  • A final zero or trailing zeros in the decimal
    portion ONLY are significant.

26
Rule 1
  • Examples
  • 26.38 (4)
  • 3 (1)
  • 4576 (4)
  • 5.78913 (6)

27
Rule 2
  • Examples
  • 2809 (4)
  • 45.09 (4)
  • 10.032 (5)

28
Rule 3
  • Examples
  • 0.00500 (3)
  • 0.0320 (3)
  • 12.3500 (6)
  • 2.30 x 102 (3)
  • 4.500 x 103 (4)

29
Zeros that DONt count.
  • Examples
  • 0.0050 (2) Space holding zeros.
  • 0.45 (2) The courteous zero.
  • 24,000 (2) Trailing zeros in a whole number.

30
Exact Numbers
  • Exact Numbers have an infinite number of
    significant figures.
  • Ex) of people in a room 25
  • Ex) 100 years in a century
  • Ex) 500 sheets of paper in one ream

31
YepSome Practice Problems
  • 3.0800
  • 0.00418
  • 7.09 x 10-5
  • 91,600
  • 0.003005
  • 3.200 x10 9
  • 250
  • 780,000
  • 0.0101
  • 0.00800

5 3 3 3 4 4 2 2 3 3
32
Adding and Subtracting with Significant Figures
  • The answer is never more precise than the numbers
    used in the math.
  • ie. You can never be more precise than the least
    precise measurment.
  • Major Rule You only look at the decimal portion
    of the number.

33
Adding and Subtracting with Significant Figures
  • Rules
  • Count the number of significant digits in the
    decimal portion of each number.
  • Add or subtract in the normal fashion.
  • Round the answer to the LEAST number of places in
    the decimal portion.

34
Practice
  • 3.461728 14.91 0.980001 5.2631
  • 23.1 4.77 125.39 3.581
  • 22.101 0.9307
  • 0.04216 0.0004134
  • 564321 264321

24.61 156.8 21.170 0.04175 300000
35
Multiplication and Division with Significant
Figures
  • Rule The LEAST number of significant figures in
    any number of the problem determines the number
    of significant figures in the answer.

36
Practice
8.6 14.0 3.0 x 10 1 114 6.17 x 10 10 1500000
  • 2.5 x 3.42
  • 3.10 x 4.520
  • 2.33 x 6.085 x 2.1
  • (4.52 x 10-4) / (3.980 x 10-6)
  • (3.4617 x 107) / (5.61 x 10-4)
  • (2.34 x 102)(0.012)(5.2345 x 105)

37
Measuring withSignificant Figures
38
Measurements
  • No measurement is exact. This means there is some
    uncertainty.
  • There are always two parts to a measurement
  • Numerical part
  • Unit/label

39
Measuring with a Meter Stick
  • We know the object is greater than 2 and less
    than 3.
  • We know the object is greater than 0.8 and less
    than 0.9
  • We can also guess at one more place. So, Ill
    guess 0.04
  • Final answer 2.84 cm.

40
Meter Stick Example 1
  • What length is indicated by the arrow?
  • More than 4, less than 5.
  • More than 0.5 but less than 0.6
  • Guess at 0.00
  • So, 4.50 cm.

41
Meter Stick Example 2
  • What length is indicated by the arrow?

9.40 cm
42
Meter Stick Example 3
  • What length is indicated by the arrow?

12.34 cm
43
Measuring with a Thermometer
  • What is the temperature?
  • Greater than 15, but less than 16.
  • Guess one place. So, 0.0
  • Final answer 15.0 C

44
Thermometer Example 1
  • What is the temperature?

28.5 C
45
Thermometer Example 2
  • What is the temperature?

21.8 C
46
Thermometer Example 3
  • What is the temperature?

36.0 C
47
Measuring with aGraduated Cylinder
  • What is the volume?
  • Read to the bottom of the meniscus.
  • Greater than 30, less than 31.
  • Guess at one. So, 0.0
  • Answer 30.0 mL

48
Graduated Cylinder Example 1
  • What is the volume?

4.28 mL
49
Graduated Cylinder Example 2
  • What is the volume?

27.5 mL
50
Graduated Cylinder Example 3
  • What is the volume?

5.00 mL
51
Metric Conversions
52
Conversion of Units
  • Sometimes it is necessary to report an answer in
    a particular unit. You will need to convert.
  • Sometimes you will need to convert a measurement
    into another unit in order to work with it.
  • Even though a measurement is convert into
    different units, it still represents the same
    amount.

53
King Henry MethodKHDBdcm
  • Easy to memorize and use.
  • Doesnt work for all the problems.
  • King kilo (1000)
  • Henrys Hecto (100)
  • Dog Deka (10)
  • Bowser Base (1)
  • died deci (1/10)
  • chewing centi (1/100)
  • mothballs milli (1/1000)

54
Dimensional Analysis orConversion Factor Method
  • This method can be used for any type of problem.
  • You begin with a number to be converted and use a
    series of factors to change the unit into
    something else.
  • You must know some relationships between units.

55
Example 1
  • Convert 6.35 miles to kilometers
  • You need to know the conversion between mi and
    km.
  • 1 mi 1.6 km

56
Example 2
  • Convert 17 years into seconds.
  • Multiple steps are required.

57
Example 3
  • Change 1.0 ft2 to m2.
  • If a quantity is squared than you must use two
    conversion factors.

58
Example 4
  • Covert 52.6 g/cm3 to kg/m3.
  • Change one unit and then the other.

59
Practice
  • Express your height in meters. (Begin with your
    high in inches.)
  • If you drive an average of 60 mph to GI, how fast
    would this be in km/h?
  • How long have you been alive in seconds? (Begin
    with your age in years.)

60
More Practice
  • How much paint would be required to paint a wall
    that measures 8 ft by 15 ft? (Express your answer
    in m2.)
  • The density of water is 1 g/cm3. What is the
    density of water in kg/m3?

61
Graphing TechniquesandInterpreting Graphs
62
Steps to follow when graphing.
  • The independent variable goes on the horizontal
    axis and dependent variable goes on the vertical
    axis.
  • The independent variable is the quantity that is
    deliberately manipulated.
  • The dependent variable changes as a result of the
    independent variable being manipulated.

63
  • 2. Choose a scale that allows your graph to be as
    large as possible.
  • The scale on each axis may be different.
  • The scale must be uniform on a given axis.
  • The graph may start at (0,0), but does not have
    to.
  • 3. Label the axis.
  • 4. Place correct units on each axis.
  • 5. Title the graph.

64
  • 6. Plot the data.
  • 7. Construct a line that best represents the
    data. If it appears that the points lie in a
    straight line construct a straight line with a
    ruler. DO NOT CONNECT THE DOTS!
  • If it appears that the points follow a curved
    pattern construct a best-fit-line freehanded.

65
Three Types of Graphs
66
Linear or Direct Relationship
  • y mx b m represents slope and b represents
    the y-intercept
  • As one variable increases, so does the other.

67
Inverse Relationship
  • y 1/x
  • As one variable increases the other variable
    decreases

68
Exponential Relationship
  • y x2

69
Finding the Slope on a Linear Graph
  • Pick two points on the line. (They may not always
    be data points.) Pick points that are separated.
  • Slope is rise over run.

70
Algebra Skills
71
Rearranging
  • One of the tasks that physics requires is being
    able to rearrange equations.
  • RememberThe reason for rearranging is to isolate
    the variable that you are looking for.
  • Basic Rule What you do to one side of the
    equation, you must do to the other side also.

72
Example v d/t
  • Solve for d
  • Multiple both sides by t. The ts on the right
    hand side cancel leaving d.
  • Therefore, d vt
  • Solve for t
  • Again, multiply both sides by t and divide both
    sides by v.
  • Therefore, t d/v

73
Example d ½ g t2
  • Solve for time.
  • Multiple both sides by 2
  • 2d gt2
  • Divide both sides by g
  • 2d/g t2
  • Square root both sides.
  • T SQR(2d/g)

74
Example E mgh ½ mv2
  • Solve for m
  • E m(gh ½ v2)
  • m E/(gh ½ v2)

75
Example 2 E mgh ½ mv2
  • Solve for h
  • E ½ mv2 mgh
  • h (E ½ mv2 )/mg

76
Example 3 E mgh ½ mv2
  • Solve for v
  • E mgh ½ mv2
  • 2(E mgh ) mv2
  • 2(E mgh )/m v2
  • v SQR2(E mgh )/m
About PowerShow.com