lesson 2-math review scientific notation, significant...

Math ReviewMath Review

�� Science and ReligionScience and Religion

�� Metric SystemMetric System

�� Scientific NotationScientific Notation

Significant FiguresSignificant Figures�� Significant FiguresSignificant Figures

Areas of PhysicsAreas of Physics

�� MechanicsMechanics

�� ThermodynamicsThermodynamics

�� Waves Waves

OpticsOptics�� OpticsOptics

�� ElectromagnetismElectromagnetism

�� RelativityRelativity

�� Quantum MechanicsQuantum Mechanics

Physics is the Most Physics is the Most Basic of SciencesBasic of Sciences

�� the ideas of physics extend into more the ideas of physics extend into more complex sciences.complex sciences.

�� you can better understand science in you can better understand science in general if you understand physics.general if you understand physics.general if you understand physics.general if you understand physics.

�� it is about the nature of basic things like it is about the nature of basic things like forces, energy, and motion.forces, energy, and motion.

�� underneath biology is chemistry and underneath biology is chemistry and underneath chemistry is physics.underneath chemistry is physics.

Science and ReligionScience and Religion

�� What is Religion?What is Religion?

What is Science?What is Science?�� What is Science?What is Science?


�� The word religion derives from the Latin The word religion derives from the Latin word to bind or to ligate (tie).word to bind or to ligate (tie).

�� It means bind to the gods It means bind to the gods �� It means bind to the gods It means bind to the gods


�� The word science comes from the Latin The word science comes from the Latin word for knowledgeword for knowledge

�� It occurs in the word consciousIt occurs in the word conscious�� It occurs in the word consciousIt occurs in the word conscious


�� Religion is a belief in somethingReligion is a belief in something

�� The belief is not necessarily substantiated The belief is not necessarily substantiated by physical or material evidenceby physical or material evidence

�� Religious knowledge obtained through Religious knowledge obtained through �� Religious knowledge obtained through Religious knowledge obtained through holy writings, authority, revelations and holy writings, authority, revelations and religious experiencesreligious experiences

�� Religious people have faith or trust in such Religious people have faith or trust in such knowledge knowledge


�� Religious knowledge is qualitative not Religious knowledge is qualitative not quantitative.quantitative.

�� Religious knowledge is not gotten through Religious knowledge is not gotten through measurement measurement measurement measurement

�� In religion knowledge is taken as either In religion knowledge is taken as either true or false. true or false.

�� Religious knowledge is neither Religious knowledge is neither progressive, nor tentative. progressive, nor tentative.


�� Scientific knowledge is a relationship Scientific knowledge is a relationship between observationsbetween observations

�� The observations are subject to The observations are subject to refinementrefinementrefinementrefinement

�� Scientific knowledge is progressive and Scientific knowledge is progressive and tentativetentative

�� Scientific knowledge is neither true nor Scientific knowledge is neither true nor false, but rather consistent with the false, but rather consistent with the observations and consistent with prior observations and consistent with prior knowledgeknowledge


�� Science formulates quantifiable questionsScience formulates quantifiable questions

�� Science uses units, numbers, direction Science uses units, numbers, direction along with mathematics to express along with mathematics to express knowledgeknowledgeknowledgeknowledge

�� Numbers are quantitative.Numbers are quantitative.

�� Units are not a quality. Units are Units are not a quality. Units are dimensions representing time, energy, dimensions representing time, energy, weight, volume, length, brightness. weight, volume, length, brightness. Dimensions are independent variables Dimensions are independent variables

Assumptions of ScienceAssumptions of Science

�� The world is real. The world is real.

�� The real world is knowable and The real world is knowable and comprehensible. comprehensible.

�� There are laws that govern the real world. There are laws that govern the real world. �� There are laws that govern the real world. There are laws that govern the real world.

�� Those laws are knowable and Those laws are knowable and comprehensible. comprehensible.

�� Those laws don't [radically] change Those laws don't [radically] change according to place or time, since the early according to place or time, since the early stages of the stages of the big bangbig bang. .

Assumptions of ScienceAssumptions of Science

�� Nature is understandable Nature is understandable

�� The rules of logic are valid The rules of logic are valid

�� Language is adequate to describe the natural Language is adequate to describe the natural �� Language is adequate to describe the natural Language is adequate to describe the natural realm realm

�� Human senses are reliable.Human senses are reliable.

�� Mathematical rules are descriptive for the Mathematical rules are descriptive for the physical worldphysical world

Basic Assumptions of ScienceBasic Assumptions of Science

�� Assumptions are accepted without proofAssumptions are accepted without proof

�� Form the basis of all scientific thinkingForm the basis of all scientific thinking

�� In other words, the basic assumptions of science In other words, the basic assumptions of science are accepted on faith. Interesting.are accepted on faith. Interesting.

Limitations of ScienceLimitations of Science

�� Science can't answer questions about value. For Science can't answer questions about value. For example, there is no scientific answer to the example, there is no scientific answer to the questions, "Which of these flowers is prettier?" questions, "Which of these flowers is prettier?" or "which smells worse, a skunk or a skunk or "which smells worse, a skunk or a skunk cabbage?" And of course, there's the more cabbage?" And of course, there's the more cabbage?" And of course, there's the more cabbage?" And of course, there's the more obvious example, "Which is more valuable, one obvious example, "Which is more valuable, one ounce of gold or one ounce of steel?" Our ounce of gold or one ounce of steel?" Our culture places value on the element gold, but if culture places value on the element gold, but if what you need is something to build a what you need is something to build a skyscraper with, gold, a very soft metal, is pretty skyscraper with, gold, a very soft metal, is pretty useless. So there's no way to scientifically useless. So there's no way to scientifically determine valuedetermine value..


�� Science can't answer questions of morality. The problem Science can't answer questions of morality. The problem of deciding good and bad, right and wrong, is outside of deciding good and bad, right and wrong, is outside the determination of science. This is why expert the determination of science. This is why expert scientific witnesses can never help us solve the dispute scientific witnesses can never help us solve the dispute over abortion: all a scientist can tell you is what is going over abortion: all a scientist can tell you is what is going over abortion: all a scientist can tell you is what is going over abortion: all a scientist can tell you is what is going on as a fetus develops; the question of whether it is on as a fetus develops; the question of whether it is right or wrong to terminate those events is determined right or wrong to terminate those events is determined by cultural and social rulesby cultural and social rules----in other words, morality. in other words, morality. The science can't help here.The science can't help here.

��


�� Science can't help us with questions about Science can't help us with questions about the supernatural. The prefix "super" means the supernatural. The prefix "super" means "above." So supernatural means "above (or "above." So supernatural means "above (or "above." So supernatural means "above (or "above." So supernatural means "above (or beyond) the natural." The toolbox of a beyond) the natural." The toolbox of a scientist contains only the natural laws of the scientist contains only the natural laws of the universe; supernatural questions are outside universe; supernatural questions are outside their reach. their reach.

�� A statement a scientist should not make (if he or she is A statement a scientist should not make (if he or she is well trained and is not manipulating you):well trained and is not manipulating you):

�� Evolution is true.Evolution is true.�� The Big Bang happened.The Big Bang happened.

�� Better statements:Better statements:

�� The theory of evolution is by far the best model we have The theory of evolution is by far the best model we have to explain both the fossil evidence and the genetic to explain both the fossil evidence and the genetic evidence with regard to the origin of all species.evidence with regard to the origin of all species.

�� The Big Bang model is in dramatic agreement will all The Big Bang model is in dramatic agreement will all known facts about the origin and history of the universe.known facts about the origin and history of the universe.

�� Science seeks consistency, not “truth.” What is the Science seeks consistency, not “truth.” What is the simplest and most consistent explanation of the simplest and most consistent explanation of the observation.observation.


�� Religion and science ask different kinds of Religion and science ask different kinds of questions and define words differentlyquestions and define words differently

�� Religion and science appear as if they Religion and science appear as if they �� Religion and science appear as if they Religion and science appear as if they were two were two incommensurateincommensurate paradigms paradigms addressing the identical information arenaaddressing the identical information arena

�� Questions science asks and attempts to answer:Questions science asks and attempts to answer:

–– When, where, how many, why (by what means)When, where, how many, why (by what means)

–– How does a living thing function?How does a living thing function?

–– What are the fundamental forces?What are the fundamental forces?

�� Question religion asks and attempts to answer:Question religion asks and attempts to answer:

–– Why am I here?Why am I here?

–– Is that the right thing to do?Is that the right thing to do?

–– How valuable am I?How valuable am I?–– How valuable am I?How valuable am I?

–– Does God exist? Does God act (theism)?Does God exist? Does God act (theism)?

–– Will that God respond if I pray?Will that God respond if I pray?

�� Questions both ask (but by different means)Questions both ask (but by different means)

–– How and when did life originate?How and when did life originate?

–– How and when did the universe originate?How and when did the universe originate?


�� Religion offers certaintyReligion offers certainty

�� Science is tentativeScience is tentative

Should I take vitamins? What’s the best birthing method? Should I take vitamins? What’s the best birthing method?

Is the Pritikan diet the best or is a vegan diet better?Is the Pritikan diet the best or is a vegan diet better?

�� Though science is tentative; it is also efficacious Though science is tentative; it is also efficacious and progressiveand progressive

Unanswered questions which seem Unanswered questions which seem to relate to scienceto relate to science

�� Consciousness (what is consciousness and why are Consciousness (what is consciousness and why are we conscious?)we conscious?)

�� Origins of life Origins of life

�� Origin of the universe. Why is there anything (as Origin of the universe. Why is there anything (as opposed to nothing)opposed to nothing)

KnowledgeKnowledge�� Are there questions asked by art or religion? Are there questions asked by art or religion?

�� Are those question understood by Science?Are those question understood by Science?

�� Can science answer the questions asked by Can science answer the questions asked by painting or religion?painting or religion?

�� Can science decide which painting or which Can science decide which painting or which �� Can science decide which painting or which Can science decide which painting or which musical score is great and which is dross?musical score is great and which is dross?

�� Do science, religion and art contradict each Do science, religion and art contradict each other?other?

Scientific MethodScientific Method

�� Make observationsMake observations

�� Define the problem (Ask a question).Define the problem (Ask a question).

�� Develop a Hypothesis Develop a Hypothesis

Test hypothesis with experimentsTest hypothesis with experiments�� Test hypothesis with experimentsTest hypothesis with experiments

�� Conclusion Conclusion –– an “interpretation” of an “interpretation” of experimental results.experimental results.

A Scientific MethodA Scientific Method

�� Length Length –– 1 meter (m)1 meter (m)

�� Mass Mass –– 1 kilogram (kg)1 kilogram (kg)

�� Time Time –– 1 second (s)1 second (s)

SI UnitsSI Units

�� Time Time –– 1 second (s)1 second (s)

�� Temperature Temperature -- 1 kelvin (K)1 kelvin (K)

�� Derived Units Derived Units

–– Combination of units`Combination of units`

Rule #4Rule #4--No SwearingNo Swearing

Cussing in PhysicsCussing in Physics

The following 4The following 4--Letter Words are forbidden Letter Words are forbidden here:here:

InchInch MileMileInchInch MileMile

FootFoot PintPint

YardYard AcreAcre

And we never use the And we never use the Big FBig F (use (use °°C)C)

Please keep in clean in andPlease keep in clean in and

MetricMetric

• Precision-2 Meanings

• The repeatability of a measurement.

• The number of significant digits in the measurement.

Accuracy Vs. PrecisionAccuracy Vs. Precision• Accuracy

• How close your

measurement is to an

accepted value for that

measurement.

• Depends on how

carefully the measurement.

�Depends on the equipment used.

carefully the

measurement was

made.

Accuracy vs. PrecisionAccuracy vs. Precision

Low Precision, Low AccuracyLow Precision, Low Accuracy

High Precision, Low Accuracy

Accuracy vs. PrecisionAccuracy vs. Precision

Low Precision, High AccuracyLow Precision, High Accuracy

High Precision, High AccuracyHigh Precision, High Accuracy

Powers of TenPowers of Ten

�� Used for very large and very small Used for very large and very small number number

�� Precision expressionPrecision expression

ppico-10-12 kkilo-103

ffemto-10-15

dadeka-101aatto-10-18

hhecta-102

ddeci-10-1 Eexa-1018

ccenti-10-2 Ppeta-1015

mmilli-10-3 Ttera-1012

µmicro-10-6 Ggiga-109

nnano-10-9 Mmega-106

ppico-10-12 kkilo-103

Scientific NotationScientific Notation

A short-hand way of writing

large numbers without large numbers without

writing all of the zeros.

The Distance From the Sun to The Distance From the Sun to the Earththe Earth

238,857 miles

(384,392 kilometers) (384,392 kilometers)

You could say…You could say…

384,392 km or

3.84392x105 km

Step 1Step 1

�� Move decimal leftMove decimal left

�� Leave only one number in front of decimalLeave only one number in front of decimal

Step 2Step 2

�� Write number without zerosWrite number without zeros

Step 3Step 3

�� Count how many places you moved Count how many places you moved decimaldecimal

�� Make that your power of tenMake that your power of ten

The power of

ten is 7 because

the decimal

moved 7 places.moved 7 places.

��93,000,000 93,000,000 ------Standard Form Standard Form

��9.3 x 109.3 x 1077 ------Scientific NotationScientific Notation

Practice ProblemPractice Problem

1)1) 98,500,000 = 9.85 x 1098,500,000 = 9.85 x 10? ?

Write in scientific notation.

Decide the power of ten.

9.85 x 107

2)2) 64,100,000,000 = 6.41 x 1064,100,000,000 = 6.41 x 10??

3)3) 279,000,000 = 2.79 x 10279,000,000 = 2.79 x 10??

4)4) 4,200,000 = 4.2 x 104,200,000 = 4.2 x 10??

6.41 x 1010

2.79 x 108

4.2 x 106

More Practice ProblemsMore Practice Problems

1)1) 734,000,000 = ______ x 10734,000,000 = ______ x 1088

2)2) 870,000,000,000 = ______x 10870,000,000,000 = ______x 101111

3)3) 90,000,000,000 = _____ x 1090,000,000,000 = _____ x 101010

On these, decide where the decimal will be moved.

1) 7.34 x 108 2) 8.7 x 1011 3) 9 x 1010

Complete Practice ProblemsComplete Practice Problems

1)1) 50,00050,000

2)2) 7,200,0007,200,000

802,000,000,000802,000,000,000

Write in scientific notation.

3)3) 802,000,000,000802,000,000,000

1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

Scientific Notation to Standard Scientific Notation to Standard FormForm

Move the decimal to the right

3.4 x 105 in scientific notation3.4 x 105 in scientific notation

340,000 in standard form

3.40000 --- move the decimal

Write in Standard FormWrite in Standard Form

��6.27 x 106.27 x 1066 ��6,270,0006,270,000

��9.01 x 109.01 x 1044

��6.27 x 106.27 x 10--66

��9.01 x 109.01 x 10--44

��90,10090,100

�� .00000627.00000627

�� .000901.000901

Calculating in Scientific NotationCalculating in Scientific Notation

�� MultiplicationMultiplication–– Multiply the coefficients and add the exponentsMultiply the coefficients and add the exponents

(3.45x10(3.45x1077) x (6.25x10) x (6.25x1055))

Rewrite ProblemRewrite Problem

(3.45 x 6.25) x (10(3.45 x 6.25) x (1077 x 10x 1055))

Then multiply the coefficients and add the exponentsThen multiply the coefficients and add the exponents

21.5625x1021.5625x101212

Then change to correct scientific notation and round to Then change to correct scientific notation and round to correct significant digitscorrect significant digits

2.16x102.16x101313


�� DivisionDivision–– Divide the coefficients and subtract the exponentsDivide the coefficients and subtract the exponents

–– Divide 3.5x10Divide 3.5x1088 by 6.6x10by 6.6x1044

–– Rewrite the problem as:Rewrite the problem as: 3.5x103.5x1088

6.6x106.6x1044

–– Divide the coefficients and subtract the exponents to Divide the coefficients and subtract the exponents to get: 0.530303x10get: 0.530303x1044

–– Change to correct scientific notation and round to Change to correct scientific notation and round to correct significant digits to get: 5.3x10correct significant digits to get: 5.3x1033


�� Adding and SubtractingAdding and Subtracting

–– When adding or subtracting in scientific When adding or subtracting in scientific notation, you must express the numbers as notation, you must express the numbers as the same power of 10the same power of 10the same power of 10the same power of 10

–– Add 3.76x10Add 3.76x1044 and 5.5x10and 5.5x1022

–– Move the decimal to change 5.5x10Move the decimal to change 5.5x102 2 to to 0.055x100.055x1044

–– Following the rules for rounding, our final Following the rules for rounding, our final answer is 3.815x10answer is 3.815x1044

Significant FiguresSignificant Figures

�� Consist of all the digits known with Consist of all the digits known with certainty plus one final digit, which is certainty plus one final digit, which is somewhat uncertain or is estimated.somewhat uncertain or is estimated.

�� Uncertainty in CalculationsUncertainty in Calculations�� Uncertainty in CalculationsUncertainty in Calculations

–– Measured quantities are often used in Measured quantities are often used in calculations. The precision of the calculation is calculations. The precision of the calculation is limited by the precision of the measurements limited by the precision of the measurements on which it is basedon which it is based

EXAMPLEEXAMPLE

�� If you measure the length of a pen with a If you measure the length of a pen with a ruler and found it to be less than halfway ruler and found it to be less than halfway between 14.1 and 14.2 cm long…would it between 14.1 and 14.2 cm long…would it be 14.112, 14.178, or 14.145 cm long? be 14.112, 14.178, or 14.145 cm long? be 14.112, 14.178, or 14.145 cm long? be 14.112, 14.178, or 14.145 cm long?

�� The third digit in the length must be The third digit in the length must be estimated. This estimated digit tells estimated. This estimated digit tells anyone reading the measurement that the anyone reading the measurement that the pen is no longer that 14.2 cm. pen is no longer that 14.2 cm. pen is no longer that 14.2 cm. pen is no longer that 14.2 cm.

Present=pacific Absent=atlanticPresent=pacific Absent=atlantic

0.43210.4321

��Present=pacificPresent=pacific

2904029040

��Absent=atlanticAbsent=atlantic

0.6930200.693020

200005200005

How many significant figures are in How many significant figures are in each of the following?each of the following?

��1. 2900000001. 290000000

��2. 0.0003142. 0.000314

2

3��2. 0.0003142. 0.000314

��3. 0.1899000003. 0.189900000

��4. 500000.4. 500000.

9

3

6

Exact numbers=no sig. fig.Exact numbers=no sig. fig.

��7 days = 1 week7 days = 1 week

��$25.00 have exactly 25 $25.00 have exactly 25 dollarsdollarsdollarsdollars

��12 inches in 1 foot12 inches in 1 foot

��60 minutes in 1 hour60 minutes in 1 hour

��100 cm in 1 meter100 cm in 1 meter

Sig Figs with Estimation Sig Figs with Estimation and Scientific Notationand Scientific Notation

�� Only count the number that is knownOnly count the number that is known

–– 10.56 x1010.56 x101212

–– 10.56+/10.56+/-- 0.0010.001

How to determine accuracy and How to determine accuracy and precision with uncertaintiesprecision with uncertainties

�� Two students measure the mass of an Two students measure the mass of an object.object.

�� Student one calculated the mass as Student one calculated the mass as 67.01+/67.01+/-- 0.0080.00867.01+/67.01+/-- 0.0080.008

�� Student two calculated the mass as Student two calculated the mass as 68.145+/68.145+/-- 0.0010.001

–– Mass of the object was actually 68.087gMass of the object was actually 68.087g

–– Which is more precise and which is most Which is more precise and which is most accurate.accurate.

Find the % of the uncertaintiesFind the % of the uncertainties

–– Formula:Formula:�� 100 x uncertainty/value for measurement100 x uncertainty/value for measurement

–– Student oneStudent one�� 67.01+/67.01+/-- 0.0080.008�� 67.01+/67.01+/-- 0.0080.008

�� 100 x 0.008/67.01 = 0.012100 x 0.008/67.01 = 0.012

–– Student two Student two �� 68.145+/68.145+/-- 0.0010.001

�� 100 x .001/68.145 = 0.0015100 x .001/68.145 = 0.0015

–– Mass of the object was actually 68.087gMass of the object was actually 68.087g

–– Which student was more precise?Which student was more precise?

–– Which student was more accurate?Which student was more accurate?

Calculating with Sig. FigsCalculating with Sig. Figs

When multiplying or dividingWhen multiplying or dividing--Limit the Limit the answer to the same number of significant answer to the same number of significant digits that appear in the original data with digits that appear in the original data with the fewest number of significant digits the fewest number of significant digits the fewest number of significant digits the fewest number of significant digits

3.22 3.22 ×× 2.1 cm = 6.762 2.1 cm = 6.762

Significant Number = 6.8 Significant Number = 6.8

3.22 3.22 ÷÷ 2.1 = 1.5333 2.1 = 1.5333

Significant Number = 1.5Significant Number = 1.5

When adding or subtracting. Limit the When adding or subtracting. Limit the answer to the same number of decimal answer to the same number of decimal places that appear in the original data places that appear in the original data with the fewest number of decimal places with the fewest number of decimal places

24.686 m + 2.343 m + 3.21 m = 30.239 m24.686 m + 2.343 m + 3.21 m = 30.239 m


25.122 25.122 –– 5.67 5.67 –– 4.56 = 14.8924.56 = 14.892


Calculating with Sig. FigsCalculating with Sig. Figs

�� Significant Figs in Combined OperationsSignificant Figs in Combined Operations

–– Remember your order of operationRemember your order of operation

–– Be sure to remember to include only the sig. Be sure to remember to include only the sig. figs. before going on to the next operation figs. before going on to the next operation figs. before going on to the next operation figs. before going on to the next operation

0.91 + 1.2 + 8.40.91 + 1.2 + 8.4 ==

3.7003.700

10.51 =

3.700

2.8405

2.84

Musical ReviewMusical Review

�� Big Big Sig.FigsSig.Figs..

�� Where the Heck to RoundWhere the Heck to Round

HomeworkHomework

�� Scientific NotationScientific Notation

�� Significant Numbers WorksheetSignificant Numbers Worksheet

lesson 2-math review scientific notation, significant...

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