units, metric system, conversions, uncertainty, significant figures, scientific notation &

8/14/2019 Units, Metric System, Conversions, Uncertainty, Significant Figures, Scientific Notation &

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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!


2/27

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.


3/27

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


4/27

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


5/27

AHHHH! This

chocolate milk is

killing me!

X X


6/27

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


7/27

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


8/27

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


10/27

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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12/27

Accurate or precise?

Precise but not accurate Accurate AND precise

Not accurate NOR precise Accurate (on average)

but NOT precise


13/27

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?


15/27

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


16/27

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


17/27

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


18/27

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


19/27

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


20/27

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


21/27

Measurement - Mass

On an electric

balance, report all

the digits,knowing that the

last digit contains

an estimate0.042 g


22/27

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


23/27

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)


24/27

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


25/27

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

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