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

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
• 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
• 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
• 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

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

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
• What is the volume?
• Read to the bottom of the meniscus.
• Greater than 30, less than 31.
• Guess at one. So, 0.0

48
• What is the volume?

4.28 mL
49
• What is the volume?

27.5 mL
50
• 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

60
More Practice
• How much paint would be required to paint a wall
in m2.)
• The density of water is 1 g/cm3. What is the
density of water in kg/m3?

61
Graphing TechniquesandInterpreting Graphs
62
• 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