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Units, Metric System,Units, Metric System,
Conversions, Uncertainty,Conversions, Uncertainty,
Significant Figures,Significant Figures,
Scientific Notation &Scientific Notation &
Dimensional AnalysisDimensional Analysis
And not necessarily in that order!
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Warm Up
You read on the internet that a group identified as the
Pleiadians and other cosmic Beings of Light use
tachyons as their basic source of energy: as a hyper
drive for their beam ships by creating hyperspace
wormholes, for healing, information transmission
and for other purposes. What further information
would you need to know to decide whether or notthis was in the realm of science of not.
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What unit should you use?
24
22
20
18
16
14
12
10
8
6
4
Luminous
Intensity
candela
Time seconds
Electricity
Ampere
Temp Kelvin
Mass
kilograms
Length meters
Amount of
substance mol
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MeterStandardized: 1983
Measures: LengthDefinition: The distance traveled by light in a vacuum in 1/299,792,458 second Second
Standardized: 1967Measures: TimeDefinition: The time it takes for a cesium-133 atom to cycle 9,192,631,770 times between two specific quantum states
AmpereStandardized: 1948Measures: Electrical current
Definition: The current required to create a force of 2 x 10
-7
newtons per meter between two parallel wires KelvinStandardized: 1954Measures: TemperatureDefinition: 1/273.16 the temperature of the triple point of water when it's simultaneously gas, liquid, and solid
MoleStandardized: 1971Measures: Amount of stuffDefinition: The number of atoms in 12 grams of carbon 12 (6.022 x 1023 )
CandelaStandardized: 1979Measures: BrightnessDefinition: The intensity of a 1/683-watt yellow-green light spread over a square meter, seen from a meter away
KilogramStandardized: 1889Measures: MassDefinition: Standard based on a physical sample of platinum-iridium metal held at the International Bureau of Weights &Measures in Paris, France.
SI UnitsSI Units
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AHHHH! This
chocolate milk is
killing me!
X X
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Metric Conversion FactorsPrefix Multiplied By Symbol Conversions to Know
Giga 109 G 1 gigabase = 1 x 109 base
1 megabase = 1 x 106 base
1 kilobase = 1 x 103 base
1 base = 100 centibase
1 base = 1000 millibase
1 base = 1 x 106 microbase
1 base = 1 x 109 nanobase
Mega 106 M
Kilo 1000 k
Hecto 100 hDeka 10 da
Base unit:
m, L, g, etc1 m, L, g
Deci 0.1 dCenti 0.01 c
Milli 0.001 m
Micro 10-6 or r
Nano 10-9
n
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Scientific Notation - Why?
It is easier to write
Calculations are simplified
Significant figures are clear
6.022x1023
is so much easier to write than
602,200,000,000,000,000,000,000
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Scientific Notation How?
Converting numbers to scientific notationMove the decimal point until there is only one digit(a non-zero one) to the left of it.
0.00340603.4060
Keep track of the number of places you moved thedecimal, and write the number as asuperscriptoverthe number ten.
three spaces;3.4060 x 103
If you moved the decimal to the right, the exponent
becomes negative; if to the left, then it remainspositive.
was moved right;
3.4060 x 10-3
Allsignificant figures from the original numbermust be kept in scientific notation!
five sig figs3.4060 x 10-3
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sdrawkcaB gnioG
Converting from scientific notation to regular
numbers
Move the decimal point the number ofplaces left (if negative exponent) or right (ifpositive exponent) that is indicated in thepower of ten. Add extra zeros forplaceholders if necessary.
7.45 x 10
4
74,500
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Vocabulary
Accuracy: how close a measurement is to the known,accepted or correct value
Example: A student measures the temperature of
boiling water to be 100.0CPrecision: how close several measurements are to each
other
Example: Six different students measure thetemperature of boiling water to be 98.2C, 98.1C,
98.0C, 98.1C, 98.3C, 98.2C.
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Accurate or precise?
Precise but not accurate Accurate AND precise
Not accurate NOR precise Accurate (on average)
but NOT precise
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Striving for Accuracy &Precision
For each of the following scenarios
1. Discuss whether or not the resulting measurements will be precise.Why?
2. Discuss whether or not we can know if the measurements areaccurate. Why?
Scenario #1:
An instrument is mis-calibrated, and one person uses it to take the samemeasurement multiple times.
Scenario #2
Many people use the same correctly calibrated instrument to take thesame measurement multiple times.
Scenario #3
One person takes the same measurement multiple times but uses manydifferent instruments of the same type.
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Estimating
Precision can also refer to how well you can know ameasured number or how many decimal places (sig.
figs) you can give a measurement
Not all measuring devices have the same precision.Not all measurements will be whole numbers. It is
important to be able to estimate and interpolate.
Look back at your warm up data, convert yourmarking measurements to centimeters
How much precision (how many digits) can you
really claim to know?
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Significant FiguresWhy arent all figures significant?
Rules Examples
1. All non-zero digits are always significant. All counting numbers aresignificant and have an infinite number of significant figures.
8.314 Latm/molK22.4 L/mol1842 Gunn students
2. Zeros between non-zeros are always significant. 2005 years$10.99
12.011 g/mol carbon3. Zeros in front of non-zeros are not significant. 0.028
0.0000109 September
4. Zeros at the end of a number and to the right of a decimal aresignificant.
1.0000 mm2.80 years
5. Zeros at the end of a number and to the left of a decimal may or may notbe significant.
Hints: Zeros that are counted or measured are significant;Zeros that hold places are not.
Use scientific notation or a decimal point for clarity.
20002000 AD2000 gallons2.0x103 gallons2000. gallons
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Atlantic Pacific Rule
a. Decimal present count from the
Pacific side
Decimal absent count from theAtlantic side
b. Find the first non-zero digit
c. All other digits are significant
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Practice
How many
significant figures in
each of thefollowing numbers?
0.0026701 m 5
19.0550 kg 6
3500 V 2
1,809,000 L 4
0.86250 g 5
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Warm Up!
Warm Up: How many significant figures
are in the following numbers ?
2.0051, 2099623002, 0.00203020400, 0.15000, 100,000.00000, 20409595000.0,
0.0000000000001
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Measurement - Volume
Always use agraduated cylinder
Bring it to your eye
levelRead the bottom of
the meniscus
Report the smallest
calibration plus one
estimated digit
21.6 ml
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Measurement -Temperature
Mercury adheres better to
itself than the glass, so the
meniscus goes the other
way.Read the top of the
meniscus.
Report the smallestcalibration plus one
estimated digit
24
22
20
18
16
14
12
10
8
6
4
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Measurement - Mass
On an electric
balance, report all
the digits,knowing that the
last digit contains
an estimate0.042 g
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Measurement - length
Use a ruler with thefinest markings
practical for the
application.
Line the object up
with the 0.
Report the smallest
calibration plus one
estimated digit
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Math with Significant FiguresMath with Significant FiguresOperation Rule Example
Addition orSubtraction
Keep the number of significant figures to theleast measured place value.
102kg + 1.2kg = 103.2kg 103kg
10.99m - 0.564m = 10.426m _____
Multiplication orDivision
Keep the number of significant figures of thenumber with the fewest digits.
102kg * 1.2kg = 122.4 kg2
120 kg2 or 1.2x102 kg2
10.99 0.564 = 19.4858416 _____
Combination ofoperations.
Follow the rules for order of operations(Please Excuse My Dear Aunt Sally) and keeptrack of the number of significant figures youwould have at each step, but dont round until
the end.Remember counting numbers are infinitely
significant!
0.185(1,627.3 + 450) 8 = ??0.185(2077.3) 8 0.185(2077)8
384.3005 8 384 8376.3005 376
10(26.127*0.95 + 15.5*0.05) = ??(assume 10 is a counting number)
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Appropriate Metric Units
For each of the following, assign appropriate units ofmetric measurement. Use any necessary prefixes.
Length of a bus
Mass of a dog
Volume of your key chain & keysWidth of the United States
Mass of a pencil
Volume of water in a lake
Depth of a tissue box
Mass of a grain of sand
Volume of water in a tub
Width of a wire
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Dimensional AnalysisProblem: How many seconds are in a year?
Identify your starting and ending units. Know where
you are starting from and where you are going to.
Starting unit: year ending unit: seconds
2. Write down your starting value on the left hand side of
your work space, and your ending value on the right
hand side. Always include units for everything!
1 year seconds
?? ??
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3. Identify any other information you may
need.
1 year = 365.25 days 1 day = 24 hours
1 hour = 60 minutes 1 minute = 60 seconds
4. Writedown each conversion with the numerator(top value in the fraction) being the unit you wantto be in, and your denominator (bottom value in the
fraction) being the unit you want to get out of or
cancel out.
year
days
1
25.365
day
hours
1
24
hour1
min60
min1
sec60
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5. When finished, carefully inspect your work
to ensure that all values are correct, have
units, and that all units cancel out except forthe last one which is the one you want to be
in.
6. Finally, multiply all values across the top anddivide by all values multiplied across the
bottom.
yeardays
125.365
day
hours
1
24
hour1
min60
min1
sec601 year = ? sec
3.1558 x 107 sec