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The Metric SystemScientific NotationSignificant

FiguresMeasuring Techniques Metric

ConversionGraphing TechniquesAlgebra Skills

A Physics ToolKit

The Metric System

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.

Advantages

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

commercial trade easier.

Some Prefixes

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.

Volume

- Volume is the amount of space that an object

takes up. - Metric units mL, L, or cm3, m3

Length

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

Scientific Notation

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

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.

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

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

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

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.

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

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.

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

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

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

continued

- Division Rule Divide the first part and subtract

the exponents. - Ex) (5.0 x 107) / (2.0 x 103) 2.5 x 104

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

Significant Figures

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.

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.

Rule 1

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

Rule 2

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

Rule 3

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

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.

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

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

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.

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.

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

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.

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)

Measuring withSignificant Figures

Measurements

- No measurement is exact. This means there is some

uncertainty. - There are always two parts to a measurement
- Numerical part
- Unit/label

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.

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.

Meter Stick Example 2

- What length is indicated by the arrow?

9.40 cm

Meter Stick Example 3

- What length is indicated by the arrow?

12.34 cm

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

Thermometer Example 1

- What is the temperature?

28.5 C

Thermometer Example 2

- What is the temperature?

21.8 C

Thermometer Example 3

- What is the temperature?

36.0 C

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

Graduated Cylinder Example 1

- What is the volume?

4.28 mL

Graduated Cylinder Example 2

- What is the volume?

27.5 mL

Graduated Cylinder Example 3

- What is the volume?

5.00 mL

Metric Conversions

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.

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)

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.

Example 1

- Convert 6.35 miles to kilometers
- You need to know the conversion between mi and

km. - 1 mi 1.6 km

Example 2

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

Example 3

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

conversion factors.

Example 4

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

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.)

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?

Graphing TechniquesandInterpreting Graphs

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.

- 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.

- 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.

Three Types of Graphs

Linear or Direct Relationship

- y mx b m represents slope and b represents

the y-intercept - As one variable increases, so does the other.

Inverse Relationship

- y 1/x
- As one variable increases the other variable

decreases

Exponential Relationship

- y x2

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.

Algebra Skills

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.

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

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)

Example E mgh ½ mv2

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

Example 2 E mgh ½ mv2

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

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