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

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The Metric SystemScientific NotationSignificant
FiguresMeasuring Techniques Metric
ConversionGraphing TechniquesAlgebra Skills
A Physics ToolKit
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The Metric System
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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.

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Advantages

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

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Some Prefixes
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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.

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Volume

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

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Length

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

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Scientific Notation
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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

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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.

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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

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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

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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

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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.

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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

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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.

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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

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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

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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

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continued

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

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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
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Significant Figures
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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.

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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.

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Rule 1

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

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Rule 2

• Examples
• 2809 (4)
• 45.09 (4)
• 10.032 (5)

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Rule 3

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

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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.

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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

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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
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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.

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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.

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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
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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.

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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)

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Measuring withSignificant Figures
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Measurements

• No measurement is exact. This means there is some
  uncertainty.
• There are always two parts to a measurement
• Numerical part
• Unit/label

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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.

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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.

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Meter Stick Example 2

• What length is indicated by the arrow?

9.40 cm
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Meter Stick Example 3

• What length is indicated by the arrow?

12.34 cm
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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

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Thermometer Example 1

• What is the temperature?

28.5 C
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Thermometer Example 2

• What is the temperature?

21.8 C
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Thermometer Example 3

• What is the temperature?

36.0 C
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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

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Graduated Cylinder Example 1

• What is the volume?

4.28 mL
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Graduated Cylinder Example 2

• What is the volume?

27.5 mL
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Graduated Cylinder Example 3

• What is the volume?

5.00 mL
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Metric Conversions
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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.

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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)

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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.

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Example 1

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

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Example 2

• Convert 17 years into seconds.
• Multiple steps are required.

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Example 3

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

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Example 4

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

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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.)

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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?

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Graphing TechniquesandInterpreting Graphs
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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.

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• 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.

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• 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.

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Three Types of Graphs
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Linear or Direct Relationship

• y mx b m represents slope and b represents
  the y-intercept
• As one variable increases, so does the other.

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Inverse Relationship

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

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Exponential Relationship

• y x2

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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.

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Algebra Skills
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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.

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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

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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)

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Example E mgh ½ mv2

• Solve for m
• E m(gh ½ v2)
• m E/(gh ½ v2)

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Example 2 E mgh ½ mv2

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

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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