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Scientific Scientific MeasurementsMeasurements
BIG NUMBERSBIG NUMBERS Scientists often work with very large Scientists often work with very large
numbers.numbers. National debt = $5,653,000,000,000National debt = $5,653,000,000,000 Bill Gates' net worth = $57,030,000,000Bill Gates' net worth = $57,030,000,000 Distance to Alpha Centauri = Distance to Alpha Centauri =
40,120,000,000,000,000 m40,120,000,000,000,000 m Distance to Andromeda Galaxy = Distance to Andromeda Galaxy =
21,800,000,000,000,000,000,000 g21,800,000,000,000,000,000,000 g Mass of Sun = Mass of Sun =
1,990,000,000,000,000,000,000,000,000,001,990,000,000,000,000,000,000,000,000,000,000 g0,000 g
Small numbersSmall numbers
Scientists often work with very small Scientists often work with very small numbers.numbers.
Radius of hydrogen atom = Radius of hydrogen atom = 0.000000000052918 m0.000000000052918 m
Mass of Hydrogen atom = Mass of Hydrogen atom = 0.0000000000000000000000016733 0.0000000000000000000000016733 gg
Mass of electron = Mass of electron = 0.000000000000000000000000000910.00000000000000000000000000091096 g096 g
What to do?What to do?
Scientific notationScientific notation – way of – way of expressing a value as the product of expressing a value as the product of a number between 1 and 10 and a a number between 1 and 10 and a power of 10.power of 10.
ExamplesExamples
300,000,000300,000,000 Move the decimal 8 places to the leftMove the decimal 8 places to the left = 3 x 10= 3 x 1088
750,000750,000 Move the decimal 5 places to the leftMove the decimal 5 places to the left = 7.5 x 10= 7.5 x 1055
More PracticeMore Practice
230,000,000230,000,000 2.3 x 102.3 x 1088
40,00040,000 4 x 104 x 1044
34,000,00034,000,000 3.4 x 103.4 x 1077
Scientific Notation cont.Scientific Notation cont.
Scientific notation can also be used Scientific notation can also be used to write out very small numbers.to write out very small numbers.
0.00050.0005 Move the decimal 4 places to the Move the decimal 4 places to the
rightright 5 x 105 x 10-4-4
More PracticeMore Practice
0.0000020.000002 = 2 x 10= 2 x 10-6-6
0.00450.0045 = 4.5 x 10= 4.5 x 10-3-3
0.0000750.000075 = 7.5 x 10= 7.5 x 10-5-5
Practice - ReversePractice - Reverse
3 x 103 x 1033
4 x 104 x 1066
3.4 x 103.4 x 1055
2.0 x 102.0 x 1044
= 3,000= 3,000
= 4,000,000= 4,000,000
= 340,000= 340,000
= 20,000= 20,000
More PracticeMore Practice
6 x 106 x 10-5-5
4.5 x 104.5 x 10-2-2
3.5 x 103.5 x 10-3-3
5.5 x 105.5 x 10-7-7
= 0.00006= 0.00006
= 0.045= 0.045
= 0.0035= 0.0035
= 0.00000055= 0.00000055
Reliability in MeasurementsReliability in Measurements
Precise Precise measurements measurements will give the will give the same results same results again and againagain and again
AccuracyAccuracy is is how close you how close you are to the are to the accepted valueaccepted value
Where would you measure?Where would you measure?
Certainty in MeasurementCertainty in Measurement
Significant digitsSignificant digits are those digits are those digits that are certain in your that are certain in your measurement plus one estimatedmeasurement plus one estimated
In order to count significant digits In order to count significant digits just count the digitsjust count the digits
5.65.6 781781 6,7786,778 What about large or small numbers?What about large or small numbers?
BIG NUMBERSBIG NUMBERS Scientists often work with very large Scientists often work with very large
numbers.numbers. National debt = $5,653,000,000,000National debt = $5,653,000,000,000 Bill Gates' net worth = $57,030,000,000Bill Gates' net worth = $57,030,000,000 Distance to Alpha Centauri = Distance to Alpha Centauri =
40,120,000,000,000,000 m40,120,000,000,000,000 m Distance to Andromeda Galaxy = Distance to Andromeda Galaxy =
21,800,000,000,000,000,000,000 g21,800,000,000,000,000,000,000 g Mass of Sun = Mass of Sun =
1,990,000,000,000,000,000,000,000,000,001,990,000,000,000,000,000,000,000,000,000,000 g0,000 g
Small numbersSmall numbers
Scientists often work with very small Scientists often work with very small numbers.numbers.
Radius of hydrogen atom = Radius of hydrogen atom = 0.000000000052918 m0.000000000052918 m
Mass of Hydrogen atom = Mass of Hydrogen atom = 0.0000000000000000000000016733 0.0000000000000000000000016733 gg
Mass of electron = Mass of electron = 0.000000000000000000000000000910.00000000000000000000000000091096 g096 g
Atlantic Pacific RuleAtlantic Pacific Rule If decimal is If decimal is AAbsent bsent
starting from the starting from the right count all digits right count all digits after the 1after the 1stst non zero non zero
If decimal is If decimal is PPresentresent starting from the left starting from the left count all digits after count all digits after the 1the 1stst non zero non zero
PracticePractice
4500 Liters4500 Liters 0.00543 grams0.00543 grams 0.00607000 seconds0.00607000 seconds 500,003 meters500,003 meters 400,000. Joules400,000. Joules 5000340035.000 Amps5000340035.000 Amps
Exact NumbersExact Numbers Remember that the rules of Sig Remember that the rules of Sig
Figs only apply to measurements Figs only apply to measurements and not exact numbers.and not exact numbers.
Years in a century Years in a century Students in a classroomStudents in a classroom Centimeters in a meterCentimeters in a meter
Rounding Sig FigsRounding Sig Figs Remember to keep the value of Remember to keep the value of
the number the same.the number the same. Remember to round up if last digit is 5 Remember to round up if last digit is 5
or more.or more.– Round 12.5 to 2 sig figsRound 12.5 to 2 sig figs– Round 56.99392882 kg to 3 sig figsRound 56.99392882 kg to 3 sig figs– Round .00027262299 mL to 4 sig figsRound .00027262299 mL to 4 sig figs– Round 303 meters to 3 sig figsRound 303 meters to 3 sig figs– Round 303 meters to 2 sig figsRound 303 meters to 2 sig figs
Multiplying / Dividing Multiplying / Dividing SigFigsSigFigs
When multiplying/dividing When multiplying/dividing measurements you are limited by measurements you are limited by the measurement with the least the measurement with the least number of significant digits.number of significant digits.
PracticePractice
Area = L x WArea = L x W Length = 6.15 mLength = 6.15 m Width = 4.026 mWidth = 4.026 m Volume = L x W x HVolume = L x W x H Volume = 3.05 x 2.10 x 0.75Volume = 3.05 x 2.10 x 0.75
SI UnitsSI Units SI units: SI units: a revised a revised
form of the metric form of the metric systemsystem
SI base unitsSI base units are are fundamental units all fundamental units all other units are based other units are based uponupon
Base UnitsBase Units
Physical Quantity Name of SI unit Symbol for SI unit
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature Kelvin K
amount of substance mole mol
luminous intensity candela cd
Derived unitsDerived units
Derived units are made from a Derived units are made from a combination of base units.combination of base units.
Examples:Examples: VolumeVolume DensityDensity
Examples of SI derived units expressed in terms of base unitsExamples of SI derived units expressed in terms of base units
Derived quantityDerived quantity SI derived unitSI derived unit
NameName SymbolSymbol
areaarea square metresquare metre mm22
volume volume cubic metre cubic metre mm33
speed, velocity speed, velocity metre per second metre per second m/sm/s
acceleration acceleration metre per second squared metre per second squared m/sm/s22
wavenumber wavenumber 1 per metre 1 per metre mm-1-1
density, mass density density, mass density kilogram per cubic metre kilogram per cubic metre kg/mkg/m33
specific volume specific volume cubic metre per kilogram cubic metre per kilogram mm33/kg/kg
current density current density ampere per square metre ampere per square metre A/mA/m22
magnetic field strength magnetic field strength ampere per metre ampere per metre A/mA/m
Converting Metric UnitsConverting Metric Units SI units based upon factors of 10 SI units based upon factors of 10 Begin with the prefix given and Begin with the prefix given and
move the decimal the same number move the decimal the same number and direction to the desired prefixand direction to the desired prefix
Know the prefixes and values: The Know the prefixes and values: The ones most important for us are Kilo ones most important for us are Kilo (1,000), Centi (.01) and Milli (.001) (1,000), Centi (.01) and Milli (.001) Others can be looked up as needed Others can be looked up as needed or will be given in the problem.or will be given in the problem.
PracticePractice
A soda can holds 355 mL A soda can holds 355 mL convert to Lconvert to L
Convert 76 km to metersConvert 76 km to meters Convert 18 mm to cmConvert 18 mm to cm A Thumb drive holds 512 A Thumb drive holds 512
Megabytes convert to KilobytesMegabytes convert to Kilobytes Violet Light has a wavelength of Violet Light has a wavelength of
430 nm convert to km430 nm convert to km
RatiosRatios
Ratios are a common way of Ratios are a common way of expressing results in Chemistryexpressing results in Chemistry
Teacher to student ratioTeacher to student ratio VelocityVelocity Population DensityPopulation Density DensityDensity Ratios of chemicals in a chemical Ratios of chemicals in a chemical
reactionreaction
Finding DensityFinding Density
Density = Mass / VolumeDensity = Mass / Volume Units are (kg/mUnits are (kg/m33) or (g/mL)) or (g/mL)
Lets calculate DensityLets calculate Density Mass = 27 kgMass = 27 kg Volume = 3.0 mLVolume = 3.0 mL Denstiy = 9.0 kg/mLDenstiy = 9.0 kg/mL
More PracticeMore Practice
Mass = 45 kgMass = 45 kg Volume = ???? mLVolume = ???? mL Density = 5.0 kg/mLDensity = 5.0 kg/mL
PracticePractice
Mass = 10.0 gMass = 10.0 g Volume of water only = 35.0 mLVolume of water only = 35.0 mL Volume of water w/ Object = 40.0 mLVolume of water w/ Object = 40.0 mL Volume of object only = __________Volume of object only = __________ Density = ______________Density = ______________
PracticePractice
An aquarium has dimensions of An aquarium has dimensions of 25.0 cm by 68.5 cm by 34.0 cm. If 25.0 cm by 68.5 cm by 34.0 cm. If the mass of the aquarium if 2.3 kg, the mass of the aquarium if 2.3 kg, calculate the density.calculate the density.
The density of air is 0.0013 g/cmThe density of air is 0.0013 g/cm33 . . How much mass does air have in a How much mass does air have in a volume of 400. cmvolume of 400. cm33??
Water & DensityWater & Density Water has a density Water has a density
of 1.0 g/ml at 4of 1.0 g/ml at 4oo C C Water’s mass in Water’s mass in
grams is equal to its grams is equal to its volume in mLvolume in mL
Any object with a Any object with a density greater will density greater will sink. . . less will floatsink. . . less will float
1cm1cm33 = 1cc = 1ml = 1cc = 1ml
There is always some error in your There is always some error in your measurement. measurement. It is unavoidable.It is unavoidable.
To calculate use the following formula:To calculate use the following formula:
% Error = ((measured value – accepted % Error = ((measured value – accepted value)/ accepted value ) X 100 %value)/ accepted value ) X 100 %
or % error = ((O - A)/A ) X 100 %or % error = ((O - A)/A ) X 100 %
PERCENT ERROR CAN BE NEGATIVE PERCENT ERROR CAN BE NEGATIVE !!!!!!In Science, a negative percent error means In Science, a negative percent error means your value was less than the accepted value. your value was less than the accepted value. This is very common in Chemistry.This is very common in Chemistry.
Percent errorPercent error
PracticePractice
• When measuring the density of gold When measuring the density of gold you find a value of 20.9 g/cmyou find a value of 20.9 g/cm33 . The . The accepted value is 19.3 g/cmaccepted value is 19.3 g/cm33
. . What What is your error ?is your error ?
Samantha S. Sloppiness measured the volume of her soda before she drank it for her midmorning snack. She measured the volume of the 12 oz. bottle to be 10 oz. What is her error ?
AnswersAnswers # 1# 1 ((20.9 – 19.3) / 19.3 ) x 100 % ((20.9 – 19.3) / 19.3 ) x 100 %
= 8.29 %= 8.29 %
Notice it is a positive number since the Notice it is a positive number since the answer was more than the real value.answer was more than the real value.
# 2# 2 ((10 – 12) / 12 ) x 100 %((10 – 12) / 12 ) x 100 % = - 16.67 % = - 16.67 %
Notice it is a negative number since the Notice it is a negative number since the answer was less than the real value.answer was less than the real value.
