Measurement & Measurement & CalculationsCalculations

Chapter 2Chapter 2

The Scientific MethodThe Scientific Method

1.1. ObservingObserving

2.2. Formulating hypothesisFormulating hypothesis

3.3. TestingTesting

4.4. TheorizingTheorizing

5.5. Publish resultsPublish results

DefinitionsDefinitions Data may be descriptive (qualitative) or Data may be descriptive (qualitative) or

numerical (quantitative).numerical (quantitative).

System- a specific portion of matter in a System- a specific portion of matter in a given region of space that has been given region of space that has been selected for study during an experimentselected for study during an experiment

Hypothesis- a testable statement gathered Hypothesis- a testable statement gathered from observing datafrom observing data

Theory- a broad generalization that Theory- a broad generalization that explains a body of factsexplains a body of facts

SI MeasurementSI Measurement

SI- System InternationalSI- System International

QuantityQuantity SymbolSymbol Unit Unit namename

AbbreviationAbbreviation

LengthLength ll MeterMeter mm

MassMass mm KilogramKilogram kgkg

TimeTime tt SecondSecond ss

Temper-Temper-

atureatureTT KelvinKelvin KK

Amount of Amount of substancesubstance

nn MoleMole molmol

Derived UnitsDerived Units

Combinations of SI base units form Combinations of SI base units form derived units.derived units.

Volume- Amount of space occupied Volume- Amount of space occupied by an objectby an object

volume= length x width x heightvolume= length x width x height

Density- The ratio of mass to volumeDensity- The ratio of mass to volume D= D= mass_ mass_ volumevolume

ProblemProblemA sample of aluminum metal A sample of aluminum metal has a mass of 8.4 grams. The has a mass of 8.4 grams. The volume of the sample is 3.1 volume of the sample is 3.1 cmcm33. Calculate the density of . Calculate the density of

aluminum.aluminum.

Conversion FactorsConversion Factors

English conversionsEnglish conversions1 gallon= 3.79 liters1 gallon= 3.79 liters

1 kilogram= 2.2 pounds1 kilogram= 2.2 pounds1 inch= 2.54 centimeters1 inch= 2.54 centimeters

1 quart= 0.95 liters1 quart= 0.95 liters1 meter= 39.37 inches1 meter= 39.37 inches

1 mile= 1608 meters= 5280 feet1 mile= 1608 meters= 5280 feet1 mole= 6.02x101 mole= 6.02x102323 molecules= 22.4 molecules= 22.4

litersliters

Conversion FactorsConversion Factors

M- mega (1000000)M- mega (1000000)

k- kilo (1000)k- kilo (1000) DR. UL:DR. UL:

h- hecta (100)h- hecta (100) If you moveIf you move

da- deca (10)da- deca (10) down the chart, down the chart,

b- base (1)b- base (1) decimal moves todecimal moves to

d- deci (.1)d- deci (.1) the right; up thethe right; up the

c- centi (.01)c- centi (.01) chart, decimal chart, decimal

m- milli (.001)m- milli (.001) moves to the moves to the left!left!

μμ- micro (.000001)- micro (.000001)

Using Scientific MeasurementsUsing Scientific Measurements

Accuracy- measured values are close Accuracy- measured values are close to the accepted value to the accepted value

Precision- measured values are close Precision- measured values are close to one another, but not necessarily to one another, but not necessarily close to the accepted valueclose to the accepted value

Percent ErrorPercent Error

Accuracy can be compared with the Accuracy can be compared with the accepted value by using percent erroraccepted value by using percent error

Percent error= Percent error= Accepted value- Experimental valueAccepted value- Experimental value x x 100100

Accepted valueAccepted value

ProblemProblemA student measures the mass A student measures the mass

& volume of a substance & & volume of a substance & calculates its density as 1.40 calculates its density as 1.40

g/mL. The correct, or g/mL. The correct, or accepted, value of the density accepted, value of the density

is 1.36 g/mL. What is the is 1.36 g/mL. What is the percent error?percent error?

Error in MeasurementError in Measurement

Some uncertainty always exists in Some uncertainty always exists in any measurementany measurement

Factors affecting the measurement Factors affecting the measurement are:are:

The skill of the measurerThe skill of the measurer The conditions of the measurementThe conditions of the measurement The measuring instrumentsThe measuring instruments

Rules for significant figuresRules for significant figures

1.1. Zeros between nonzeros are Zeros between nonzeros are significant.significant.

40.7 40.7 3 S.F. 3 S.F.

2.2. Zeros in front of nonzeros are not Zeros in front of nonzeros are not significant.significant.

0.0009 0.0009 1 S.F. 1 S.F.

3.3. Zeros at the end of a number & to Zeros at the end of a number & to the right of a decimal are significant.the right of a decimal are significant.

47.00 47.00 4 S.F. 4 S.F.

Rules con’t…Rules con’t…

4.4. Zeros at the end of a number Zeros at the end of a number without a decimal are not without a decimal are not significant.significant.

2000 2000 1 S.F. 1 S.F.

5.5. A decimal placed after the zeros A decimal placed after the zeros indicates that they are significant.indicates that they are significant.

2000. 2000. 4 S.F. 4 S.F.

ProblemProblemHow many significant figures How many significant figures

are in each of the following are in each of the following measurements?measurements?

a)a) 28.6 g28.6 gb)b) 3440. cm3440. cm

c)c) 910 m910 md)d) 0.04604 L0.04604 L

e)e) 0.0067000 kg0.0067000 kg

Scientific NotationScientific Notation

Shorthand method of writing very large & Shorthand method of writing very large & very small numbersvery small numbers

Takes the form M x 10Takes the form M x 10nn

M is greater or equal to 1 but less than 10M is greater or equal to 1 but less than 10 n is a whole number & is determined by n is a whole number & is determined by

the number of places that the decimal was the number of places that the decimal was moved to get Mmoved to get M

If decimal is moved to left, n is (+)If decimal is moved to left, n is (+)

If decimal is moved to right, n is (-)If decimal is moved to right, n is (-)

450000 = 4.5 x 10450000 = 4.5 x 1055

ProblemProblemConvert each of the following Convert each of the following

to scientific notation form:to scientific notation form:

a)a) 0.0003790.000379

b)b) 2500000025000000

c)c) 600000000000600000000000

d)d) 0.00000410.0000041