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Scientific MethodPowers of 10

Accuracy vs. PrecisionSignificant Digits

Dimensional Analysis

What is Chemistry?What is Chemistry?

Chemistry is the study of matter and the changes it undergoes. It is a science of inquiry.

We need chemistry to understand medications, cooking, and transportation issues.

Reasons to Understand Reasons to Understand ChemistryChemistry

• Be a better informed citizen so that you understand news stories about chemicals.

• So that you understand drug and chemical interactions and can make better choices about your life.

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The Most Misunderstood The Most Misunderstood Words in ScienceWords in Science

• Hypothesis, theory, skeptic, model, nature vs. nurture, significant, natural

• Observation• Hypothesis• Experiments• Conclusion

– Model– Theory– Law

Theory vs. LawTheory vs. Law

• Scientific theories explain why something happens.

• As technology changes, theories can be improved.

• Scientific laws explain how something happens.

• Laws don’t change.

Inference vs. ObservationInference vs. Observation

• Observations are made using your senses.

• Inferences are made by comparing past experiences.

Hypothesis vs. TheoryHypothesis vs. Theory

• Hypothesis– Explanation of why

something happens that must be testable.

– Requires extensive testing after which it may become a theory.

• Theory– Explanation of

why something happens that has been tested many times, is well established, and highly reliable

ModelsModels• We used models to explain hypotheses.

• What are some kinds of models that you know?

• Pure Research– Research for the

sake of knowledge

• Applied Research– Solve a specific

problem– Includes technology

Standards of MeasurementStandards of Measurement

When we measure, we use a measuring tool to When we measure, we use a measuring tool to compare some dimension of an object to a compare some dimension of an object to a standard.standard. For example, at one time the For example, at one time the

standard for length was the king’s standard for length was the king’s foot. What are some problems foot. What are some problems with this standard?with this standard?

SI measurementSI measurement• Le Système international d'unitésLe Système international d'unités • The only countries that have not The only countries that have not

officiallyofficially adopted SI are Liberia (in adopted SI are Liberia (in western Africa) and Myanmar western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but (a.k.a. Burma, in SE Asia), but now these are reportedly using now these are reportedly using metric regularlymetric regularly

• Metrication is a process that does Metrication is a process that does not happen all at once, but is not happen all at once, but is rather a process that happens rather a process that happens over time. over time.

• Among countries with non-metric Among countries with non-metric usage, the U.S. is the usage, the U.S. is the only country only country significantly holding outsignificantly holding out.. The U.S. The U.S. officially adopted SI in 1866.officially adopted SI in 1866.

15

The Base SI UnitsThe Base SI Units

Quantity Base UnitLength Meter (m)

Mass Kilogram (kg)

Time Second (s)

Temperature Kelvin (K)

Amount Mole (mol)

Electric Current Ampere (A)

Luminous Intensity Candela (cd)

Derived UnitsDerived UnitsTwo or more base units combined mathematically.Two or more base units combined mathematically.

1. Volume v = length x width x height1. Volume v = length x width x height• volume = meters x meters x metersvolume = meters x meters x meters• Three base unitsThree base units

2. Density D = mass/volume2. Density D = mass/volume• Density = kilograms/meters x meters x metersDensity = kilograms/meters x meters x meters• Four base unitsFour base units

3. Speed s = distance/time3. Speed s = distance/time• Speed = meters/secondsSpeed = meters/seconds• Two base unitsTwo base units

Measuring Volume

VolumeRemember to read the volume at the bottom of the meniscus!

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SI PrefixesPrefix Symbol Factor Scientific

NotationExample

Giga G 1,000,000,000 109 Gigameter (Gm)

Mega M 1,000,000 106 Megagram (Mg)

Kilo k 1,000 103 Kilometer (km)

Deci d 1/10 10-1 Deciliter (dL)

Centi c 1/100 10-2 Centimeter (cm)

Milli m 1/1000 10-3 Milligram (mg)

Micro µ 1/1,000,000 10-6 Microgram (µg)

Nano n 1/1,000,000,000 10-9 Nanosecond (ns)

pico p 1/1,000,000,000,000 10-12 Picometer (pm)

Metric PrefixesMetric Prefixes

Chemistry In ActionChemistry In Action

On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat.

1 lb = 1 N

1 lb = 4.45 N

“This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

What is Scientific Notation?What is Scientific Notation?

• Scientific notation is a way of Scientific notation is a way of expressing really big numbers or expressing really big numbers or really small numbers.really small numbers.

• For very large and very small For very large and very small numbers, scientific notation is more numbers, scientific notation is more concise.concise.

To change standard form to To change standard form to scientific notation…scientific notation…

• Put one non-zero digit to the left of the Put one non-zero digit to the left of the decimal point.decimal point.

• Count the number of decimal places the Count the number of decimal places the decimal point “moved” from the original decimal point “moved” from the original number. This will be the exponent on the 10.number. This will be the exponent on the 10.

• If the original number was less than 1, then If the original number was less than 1, then the exponent is negative. If the original the exponent is negative. If the original number was greater than 1, then the number was greater than 1, then the exponent is positive.exponent is positive.

ExamplesExamples

1.1. Given: 289,800,000Given: 289,800,000

2.2. Move: 2.898 (moved 8 places)Move: 2.898 (moved 8 places)

3.3. Answer: 2.898 x 10Answer: 2.898 x 1088

1.1. Given: 0.000567Given: 0.000567

2.2. Move: 5.67 (moved 4 places)Move: 5.67 (moved 4 places)

3.3. Answer: 5.67 x 10Answer: 5.67 x 10-4-4

ExamplesExamples16. Express the following in scientific

notation.a. 700 m

b. 38,000 m

c. 4,500,000 m

d. 685,000,000,000 m

e. 0.0054 kg

f. 0.00000687 kg

g. 0.000000076 kg

h. 0.0000000008 kg

ExamplesExamples

Solve the following problems on your calculator:a. 5 x 10-5m + 2 x 10-5m

b. 7 x 108m – 4 x 108m

c. 4.39 x 105kg – 2.8 x 104kg

d. 5.36 x 10-1kg – 7.40 x 10-2kg

e. (4 x 102cm) x (1 x 108cm)

f. (1 x 103cm) x (5 x 10-1cm)

g. (6 x 102g) ÷ (2 x 101cm3)

h. (4 x 10-3g) ÷ (2 x 10-2cm3)

Dimensional AnalysisDimensional Analysis

• A method of problem-solving that focuses on the units used to describe matter that uses conversion factors.

• There are always two ways to show a conversion factor!

1m = 100 cm or 100 cm = 1 m

1 km = 1000 m or 1000 m = 1 km

1 hr = 60 min or 60 min = 1 hr

How many minutes are in 2.5 hours?

Conversion factor

2.5 hr 60 min2.5 hr 60 min = 150 min = 150 min

1 hr1 hr

cancel

By using dimensional analysis, the UNITS ensure that you By using dimensional analysis, the UNITS ensure that you have the conversion right side up, and the UNITS are have the conversion right side up, and the UNITS are calculated as well as the numbers!calculated as well as the numbers!

ExamplesExamples19. Make the following conversions using the

prefix chart on #14.a. Convert 360 s to ms

 

b. Convert 4800 g to kg

 

 c. Convert 5600 dm to m

 

 d. Convert 72 g to mg

Wait a minute!

What is What is wrongwrong with the following setup? with the following setup?

1.4 day 1 day 60 min 60 sec1.4 day 1 day 60 min 60 sec

24 hr 1 hr 1 min24 hr 1 hr 1 min

Three targets Three targets with three with three arrows each arrows each to shoot.to shoot.

Can you hit the bull's-eye?Can you hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do they How do they compare?compare?

Accuracy is how close your measurements Accuracy is how close your measurements are to the accepted value.are to the accepted value.Precision is how close your measurements Precision is how close your measurements are to each other.are to each other.

Percent ErrorPercent Error

• Percent error shows how accurate your Percent error shows how accurate your measurement is:measurement is:

% Error = % Error = Accepted Value – Experimental ValueAccepted Value – Experimental Value x100 x100

Accepted ValueAccepted Value

Significant FiguresSignificant Figures

The numbers reported in a The numbers reported in a measurement are limited by the measurement are limited by the measuring toolmeasuring tool

Significant figures in a measurement Significant figures in a measurement include the measured digits plus one include the measured digits plus one estimated digitestimated digit

Rules for Significant DigitsRules for Significant Digits

• RULE 1. All non-zero digits in a RULE 1. All non-zero digits in a measured number are significant.measured number are significant.

• RULE 2. Zeros between non-zero RULE 2. Zeros between non-zero numbers are significant.numbers are significant.

• RULE 3. Other zeros are only RULE 3. Other zeros are only significant if they follow significant if they follow bothboth a decimal a decimal point point andand a non-zero digit. a non-zero digit.

ExamplesExamples

• 27. How many significant digits are in each of the following measurements?

a. 508.0L e. 0.000482mL

 

b. 820,400.0L f. 3.2587 x 10-8g

 

c. 707,000kg g. 0.0084mL

 

d. 0.049450s h. 1.0200 x 105kg

Significant Numbers in CalculationsSignificant Numbers in Calculations

A calculated answer cannot be more precise than A calculated answer cannot be more precise than the measuring tool. the measuring tool.

A calculated answer must match the least precise A calculated answer must match the least precise measurement.measurement.

Significant figures are needed for final answers Significant figures are needed for final answers fromfrom

1) adding or subtracting1) adding or subtracting

2) multiplying or dividing2) multiplying or dividing

Adding and SubtractingAdding and Subtracting

The answer has the same number of decimal The answer has the same number of decimal places as the measurement with the fewest places as the measurement with the fewest decimal places.decimal places.

25.25.22 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places

26.5426.54

answer 26.5 answer 26.5 one decimal placeone decimal place

Multiplying and DividingMultiplying and Dividing

Round (or add zeros) to the calculated Round (or add zeros) to the calculated answer until you have the same number of answer until you have the same number of significant figures as the measurement with significant figures as the measurement with the fewest significant figures.the fewest significant figures.

a. a. 2.19 X 2.19 X 4.24.2 = 9.1 = 9.19898 → 9.2 → 9.2

b. 4.311 ÷ 0.0b. 4.311 ÷ 0.077 = = 61.5857 → 61.5857 → 6600

c. c. 2.54 X 0.002.54 X 0.002828 = 2.347 → = 2.347 → 2.32.3

0.0105 X 0.00.0105 X 0.06060

ExamplesExamples30. Solve and round to the appropriate number of significant digits.

a. 43.2cm + 51.0cm + 48cm = __________________

 

b. 0.0487mg + 0.05834mg + 0.0048mg = ____________________

 

c. 5.236cm – 3.14cm =___________________

 

d. 24m x 3.26m =________________________

 

e. 53.0m x 1.53m =___________________________

 

f. 102.4m ÷ 51.2s =________________________

 

g. 168m ÷ 58s =_______________________