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Post Lab discussion (redo graph??)Post Lab discussion (redo graph??) Go over Math QuizzesGo over Math Quizzes Measuring in Science & Rearranging Measuring in Science & Rearranging Equations NotesEquations Notes

HOMEWORK: Rearranging Equations HOMEWORK: Rearranging Equations wkstwkst

Measuring in ScienceMeasuring in Science

Practicing Accurate Practicing Accurate MeasurementMeasurement

Measuring in ScienceMeasuring in Science

Why is this important?Why is this important? Understanding how to record and work Understanding how to record and work with measurements accurately is with measurements accurately is essential for success in all science-essential for success in all science-related fieldsrelated fields

SI Units (SI Units (Systeme InternationalSysteme International)) world wide system to eliminate world wide system to eliminate confusionconfusion

the metric system and the SI system can the metric system and the SI system can be used almost interchangeablybe used almost interchangeably

based on decimalsbased on decimals

SI Base UnitsSI Base Units

LengthLength

Def: the distance from one point Def: the distance from one point to anotherto another

Units: Meter, m Units: Meter, m

Different forms: cm, mm, etcDifferent forms: cm, mm, etc

SI Base UnitsSI Base Units

MassMass

Def: the measure of a quantity of Def: the measure of a quantity of mattermatter

Units: Kilograms, kgUnits: Kilograms, kg

Different forms: g, mg, etcDifferent forms: g, mg, etc

SI Unit BasesSI Unit Bases

VolumeVolume

Def: Length x Width x HeightDef: Length x Width x Height

Units: Liters, LUnits: Liters, L

Different forms: mlDifferent forms: ml

Different metric forms: mDifferent metric forms: m33, cm, cm33, cc, , cc, etc.etc.

SI Unit BasesSI Unit Bases

TimeTime Unit: secondsUnit: seconds

Temperature Temperature Unit: KelvinUnit: Kelvin

Amount of substanceAmount of substance Unit: moleUnit: mole

METRIC PREFIX AND EQUIVALENTS

Prefix Phonetic Symbol Decimal Equivalent Exponential Equivalent

Tera- Ter-uh T 1,000,000,000,000 1012

Giga- Gig-uh G 1,000,000,000 109

Mega- Meg-uh M 1,000,000 106

Kilo- Kill-uh k 1,000 103

Hecto- Hek-tuh h 100 102

Deca- Dec-uh da 10 101

Deci- Des-uh d 0.1 10-1

Centi- Sent-uh c 0.01 10-2

Milli- Mill-uh m 0.001 10-3

Micro- Mi-crow u 0.000 001 10-6

Nano- Nan-uh n 0.000 000 001 10-9

Pico- Pea-ko P 0.000 000 000 001 10-12

Femto- Fem-toe f 0.000 000 000 000 001 10-15

Atto- At-toe a 0.000 000 000 000 000 001 10-18

Percent ErrorPercent Error

Def:Def: A way to show how close A way to show how close your value is to the accepted your value is to the accepted valuevalue

= = |measured value – accepted |measured value – accepted value|value| x 100 x 100

Accepted valueAccepted value


ExampleExample Measured – 76.5 kgMeasured – 76.5 kg Accepted – 77.9 kgAccepted – 77.9 kg

Find the percent error.Find the percent error.


= =

|76.5 kg – 77.9 kg||76.5 kg – 77.9 kg| x 100 x 100

77.9 kg77.9 kg

= 1.80 %= 1.80 %

Rearranging EquationsRearranging Equations

In Chemistry we work with In Chemistry we work with numbers and a lot of different numbers and a lot of different equations. It is essential to equations. It is essential to master the skill of rearranging master the skill of rearranging equations to solve for a equations to solve for a variable.variable.

Use the following steps when Use the following steps when working with problems.working with problems.


1.1. Identify what is given to you.Identify what is given to you.2.2. Answer the question: For what are you Answer the question: For what are you

solving?solving?3.3. Set up the known equation using variables.Set up the known equation using variables.4.4. Rearrange equation, following the order of Rearrange equation, following the order of

operations, to solve for the chosen operations, to solve for the chosen variable.variable.

5.5. Plug in the proper values and units. Plug in the proper values and units. Solve Solve

Let’s refresh our memory on the Order of Let’s refresh our memory on the Order of Operations!Operations!


When you have more than one When you have more than one operation in a math problem, operation in a math problem, you must follow the correct you must follow the correct order of operations.order of operations.

Just remember:Just remember:

“ “PPlease lease EExcuse xcuse MMy y DDear ear AAunt unt SSally”ally”

Order of OperationsOrder of Operations

““PPlease” - parentheses lease” - parentheses ““EExcuse” - exponentsxcuse” - exponents ““MMy” - multipyy” - multipy ““DDear” - divideear” - divide ““AAunt” - addunt” - add ““SSally” - subtractally” - subtract

Order of OperationsOrder of Operations

When solving problems:When solving problems: Make sure the problem is copied Make sure the problem is copied down correctlydown correctly

Follow the order of operationsFollow the order of operations Do each operation Do each operation within each levelwithin each level from from left to rightleft to right

Be careful not to reuse any numbersBe careful not to reuse any numbers Continue until all operations are Continue until all operations are donedone


Example: A car crosses a major Example: A car crosses a major intersection going 48.75 intersection going 48.75 miles/hour. If the next light is miles/hour. If the next light is 1.23 miles away. How long does 1.23 miles away. How long does it take the car to reach it?it take the car to reach it?

1.1. Identify what is given to you.Identify what is given to you.

Speed = 48.75 mi/hrSpeed = 48.75 mi/hr

Distance = 1.23 milesDistance = 1.23 miles


2. Answer the question: For what are you 2. Answer the question: For what are you solving? solving?

We are solving for timeWe are solving for time

3. Set up the known equation using 3. Set up the known equation using variables.variables.

Speed = Speed = distancedistance s = s = d d

time time t t


4. Rearrange the equation to solve for chosen 4. Rearrange the equation to solve for chosen variable.variable.

s = s = dd (t)s = (t)s = d(t)d(t) t s = d t s = d

t tt t

t st s = = dd t = t = dd (s) (s) (s) (s)

s s


5. Plug in the proper values and 5. Plug in the proper values and units. Solve.units. Solve.

t = t = dd t = t = 1.23 miles1.23 miles

s s 48.75 mi/hr 48.75 mi/hr

t = 0.0252 hours t = 0.0252 hours


Example: A car is traveling at 5 Example: A car is traveling at 5 mi/hr and speeds up to 65 mi/hr. mi/hr and speeds up to 65 mi/hr. How much time does it take if the How much time does it take if the car is acceleration at a rate of 6 car is acceleration at a rate of 6 mi/hrmi/hr22..

Acceleration = Acceleration = (final velocity - (final velocity - initial velocity)initial velocity)

timetime

Significant FiguresSignificant Figures

What are they and why do we use What are they and why do we use them?them?

The number of digits in a The number of digits in a measurement that is measurement that is certaincertain, plus , plus one additional rounded off number one additional rounded off number that is that is uncertainuncertain

Significant figures indicate the Significant figures indicate the reliability of measured datareliability of measured data


Zeros in NumbersZeros in Numbers1.1. All nonzero integers are All nonzero integers are significantsignificant

2.2. All zeros to the LEFT of the firstAll zeros to the LEFT of the firstnonzero digit are not significantnonzero digit are not significant

ex: 0.0025ex: 0.0025-2 sig figs, 3 leading zeros not sig -2 sig figs, 3 leading zeros not sig figsfigs


3.3. All zeros between nonzero digits areAll zeros between nonzero digits aresignificant.significant.

Ex: 1.00003, 6 sig figsEx: 1.00003, 6 sig figs

4.4. All zeros at the end of a number thatAll zeros at the end of a number thathas a decimal point are significant.has a decimal point are significant.

Ex: 100 has 1 sig fig, 2 zeros but NO Ex: 100 has 1 sig fig, 2 zeros but NO decimaldecimal 100.00 has 5 sig figs, 4 zeros WITH 100.00 has 5 sig figs, 4 zeros WITH decimaldecimal


Identify the number of Identify the number of significant figures in the significant figures in the following examples:following examples:

1.1. 60.1 g60.1 g ____________________

2.2. 6.100 g6.100 g ____________________

3.3. 0.061 g0.061 g ____________________

4.4. 6100 g6100 g ____________________


**5.**5. Zeros at the end of a whole Zeros at the end of a whole numbernumber

that has no decimal point causethat has no decimal point cause

confusion because they may-or mayconfusion because they may-or may

not-be significant. The best way tonot-be significant. The best way to

prevent this type of confusion is toprevent this type of confusion is to

write the number in scientific write the number in scientific notation.notation.

Scientific NotationScientific Notation

Scientific notation is used to Scientific notation is used to write numbers that are very large write numbers that are very large or very small in an easier way or very small in an easier way Diameter of an atom:Diameter of an atom:

0.0000000001 m0.0000000001 m Diameter of atomic nucleus:Diameter of atomic nucleus:

0.000000000000001 m0.000000000000001 m Distance from the Earth to the Distance from the Earth to the SunSun150,000,000 km150,000,000 km


Scientific notation expresses a Scientific notation expresses a number multiplied by a power of number multiplied by a power of 10. 10.

n x 10n x 10pp

nn is a number between 1 and 10 is a number between 1 and 10 pp is a power of 10 is a power of 10Example:Example:300 is written as 3 x 10300 is written as 3 x 1022


HOW TO write numbers in scientific HOW TO write numbers in scientific notation:notation:

Move the decimal point to the left or Move the decimal point to the left or right so that only one nonzero digit is to right so that only one nonzero digit is to the left of the decimal point.the left of the decimal point.

Multiply that number by 10 raised to a Multiply that number by 10 raised to a power equal to the number of places the power equal to the number of places the decimal place was moveddecimal place was moved If you move the decimal to the left, p is If you move the decimal to the left, p is positivepositive

If you move the decimal to the right, p is If you move the decimal to the right, p is negativenegative

150 1.5 x 10150 1.5 x 1022

.0015 1.5 x 10.0015 1.5 x 10-3-3


1. 345.81. 345.8 ==

2. 0.004562. 0.00456 ==

3. 1,456,9833. 1,456,983 ==


1. 345.81. 345.8

2. 0.004562. 0.00456

3. 1,456,9833. 1,456,983

= 3.458 x 10 = 3.458 x 10 22

= 4.56 x 10 = 4.56 x 10 -3-3

= 1.456983 x 10 = 1.456983 x 10 66


1. 1. 0.0000000001 m 0.0000000001 m = 1.0 x = 1.0 x 10101010

2. 0.004562. 0.00456 ==

3. 1,456,9833. 1,456,983 ==

Uncertainty in MeasurementUncertainty in Measurement

Precision vs. AccuracyPrecision vs. Accuracy

Precision:Precision: When several measurements are taken When several measurements are taken that have close agreementthat have close agreement

Accuracy:Accuracy: How closely the measurements agree How closely the measurements agree with the true valuewith the true value


How do we measure to one place How do we measure to one place of uncertainty?of uncertainty?

What is the measurements at What is the measurements at each arrow?each arrow?

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.


How do we measure to one place How do we measure to one place of uncertainty?of uncertainty?

What is the measurements atWhat is the measurements at

each arrow?each arrow?

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.


Exact NumbersExact Numbers

Have no uncertain digits since Have no uncertain digits since there is no approximation involvedthere is no approximation involved

1 m = 1000mm1 m = 1000mm Counted items or simple fractions Counted items or simple fractions (2/3 or ¼)(2/3 or ¼)

Calculations in Significant FiguresCalculations in Significant Figures

Rounding OffRounding Off Round up if >5Round up if >5

Addition or SubtractionAddition or Subtraction When measured quantities are either When measured quantities are either added or subtracted, the answer added or subtracted, the answer retains the same number of digits to retains the same number of digits to the right of the decimal as were the right of the decimal as were present in the least precise value present in the least precise value (the number containing the fewest (the number containing the fewest number of digits to the right of the number of digits to the right of the decimal).decimal).

Calculations of Significant FiguresCalculations of Significant Figures

Multiplication and DivisionMultiplication and Division When measured quantities are When measured quantities are either multiplied or divided, the either multiplied or divided, the answer must contain the same answer must contain the same number of significant figures as number of significant figures as were present in the measurement were present in the measurement with the fewest number of with the fewest number of significant figures.significant figures.

Example CalculationsExample Calculations

AdditionAddition

46.46.11 g g 8.358.3577 g g

++106.2106.22 2 g g 160.160.6677 g 77 g

Answer with significant figures: Answer with significant figures: 106.7 g106.7 g

Example Addition/SubtractionExample Addition/Subtraction

1.1. 12.15 + 1.1 + 3.12512.15 + 1.1 + 3.125=______________=______________

2.2. 9.325 + 1.2 9.325 + 1.2 =______________=______________

3.3. 7.54 – 6.0 – 0.00947.54 – 6.0 – 0.0094=______________=______________

Example CalculationsExample Calculations

MultiplicationMultiplication

80.280.2 cmcm 33 s.f. s.f.

3.4073.407 cmcm 44 s.f. s.f.

X 0.0076X 0.0076 cmcm 2 2 s.f.s.f.

2.02.0766346766346 cmcm

Answer with significant figures: Answer with significant figures: 2.1cm 2.1cm33

Examples of Mult/DivExamples of Mult/Div

1.1. 9.325 x 1.29.325 x 1.2=______________=______________

2.2. 12.15 x 1.1 x 3.12512.15 x 1.1 x 3.125=______________=______________

3.3. 7.54 / 0.00947.54 / 0.0094=______________=______________

Converting UnitsConverting Units

When converting units, follow When converting units, follow the steps below:the steps below: Identify the starting unitIdentify the starting unit Identify the final unitIdentify the final unit Identify the conversion factor (ask Identify the conversion factor (ask yourself “How much of the starting yourself “How much of the starting unit fit in the final unit?”)unit fit in the final unit?”)

Multiply using properly labeled Multiply using properly labeled unitsunits

Cancel unitsCancel units Move decimal right or left accordinglyMove decimal right or left accordingly


Example:Example: Convert 125 grams into kilogramsConvert 125 grams into kilograms

Start unit:Start unit: gramsgrams Final unit:Final unit: kilogramskilograms Conversion factorConversion factor

There are 1000 grams in 1 kgThere are 1000 grams in 1 kg Conversion factor: final unit/start unitConversion factor: final unit/start unit

1kg/1000g1kg/1000g MultiplyMultiply

125 g X (1kg/1000g) = 0.125 g125 g X (1kg/1000g) = 0.125 g (cancel out units and move decimal point)(cancel out units and move decimal point)


Practice ProblemsPractice Problems 3.125 kg 3.125 kg =_______________g=_______________g

49.32 cm 49.32 cm =_______________m=_______________m

1.6 MW 1.6 MW =_______________W=_______________W

3 X 103 X 10-9-9 s s =_______________s=_______________s

10 X 1010 X 103 3 mm =_______________m=_______________m

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