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Metric and Metric and ConversionsConversions
Mark Ewoldsen, Ph.D.Mark Ewoldsen, Ph.D.
La Cañada High SchoolLa Cañada High School
Units and
Measurement
PhysicsMrs. Coyle
http://apod.nasa.gov/apod/image/0706/iss_sts117_big.jpg
Countries that do NOT use MetricCountries that do NOT use Metric
Basic Physics – SI UnitsBasic Physics – SI Units
QuantityQuantity UnitUnit SymbolSymbol
Length meter m
Mass gram g
Time second S
Volume liter L
SI Unit Prefixes- Part IISI Unit Prefixes- Part II
NameName SymbolSymbol FactorFactor
giga-giga- GG 101099
mega-mega- MM 101066
kilo-kilo- KK 101033
centi-centi- cc 1010-2-2
milli-milli- mm 1010-3-3
micro-micro- μμ 1010-6-6
SI Unit Prefixes for LengthSI Unit Prefixes for Length
NameName SymbolSymbol
gigametergigameter GmGm 101099 1000 Mm1000 Mm
megametermegameter MmMm 101066 1000 km1000 km
kilometerkilometer KmKm 101033 1000 m1000 m
metermeter mm 101000 1000 mm1000 mm
centimetercentimeter cmcm 1010-2-2 .01 m.01 m
millimetermillimeter mmmm 1010-3-3 1000 1000 μμmm
micrometermicrometer μμmm 1010-6-6 1000 nm1000 nm
nanometernanometer nmnm 1010-9-9 1000 pm1000 pm
picometerpicometer pmpm 1010-12-12
Scientific NotationScientific Notation
M x 10M x 10nn
or
M EnM En• M is the coefficient 1<M<10
• 10 is the base
• n is the exponent or power of 10
Other Examples:
5,450,000 = 5.45E+6 = 5.45 x 106
Numbers less than 1 Numbers less than 1 will have a will have a negative exponent.negative exponent.
A millionth of a second is:A millionth of a second is:
0.000001 sec0.000001 sec 1x10 1x10-6 -6
1.0E-61.0E-6
Solving Word ProblemsSolving Word Problems
• AnalyzeAnalyze – List knowns and unknowns.List knowns and unknowns.– Draw a diagram.Draw a diagram.– Devise a plan.Devise a plan.– Write the math equation to be used.Write the math equation to be used.
• CalculateCalculate– If needed, rearrange the equation to solve for the If needed, rearrange the equation to solve for the
unknown. unknown. – Substitute the knowns with units in the equation and Substitute the knowns with units in the equation and
express the answer with units. express the answer with units. • EvaluateEvaluate
– Is the answer reasonable?Is the answer reasonable?
How to Convert Units How to Convert Units Made EasyMade Easy
Converting10 inches to centimeters
10.0 inin
We start by writing down the units of what we want and then
number and the units given
= cmcm
Our conversion factor for this is 1 in = 2.54 cm.
Then
Multiplying by 1 does not change the value!Multiplying by 1 does not change the value!
1 inin2.54 cmcm
= 11
ConvertingInches to centimeters
10.0 inin
Our conversion factor for this is 1 in = 2.54 cm.
= cm
ConvertingInches to centimeters
10.0 inin
1 inin
2.54 cm
Our conversion factor for this is 1 in = 2.54 cm.Since we want to convert to cm, cm goes on the top.
= cm
ConvertingInches to centimeters
10.0 inin
1 inin
2.54 cm
Our conversion factor for this is 1 in = 2.54 cm.Since we want to convert to cm, cm goes on the top.Inches go on the bottom and are cancelled
= cm
ConvertingInches to centimeters
10.0 inin
1 inin
2.54 cmcm
Leaving us with cm – the unit we want.
= cmcm
ConvertingInches to centimeters
10.0 inin
1 inin
2.54 cmcm = 25.4 cmcm
Since the unit is correct, all that is left todo is the arithmetic...
The Answer
A more complex conversionkm to mhr s
80 km
hr
A more complex conversionkm to mhr s
Step 1 –Write down the number and theunit!
80 km
hr
1 hr
3600 s
A more complex conversionkm to mhr s
First we’ll convert time. Our conversion factor is1 hour = 3600 sec. Since we want hours to cancel out, we put it on the top.
= ms
80 km
hr
1 hr
3600 s
1000 m
1 km
A more complex conversionkm to mhr s
Next we convert our distance from kilometers to meters. The conversion factor is 1 km = 1000 m.Since we want to get rid of km, this time it goes on the bottom.
= ms
80 km
hr
1 hr
3600 s
1000 m
1 km=
A more complex conversionkm to mhr s
Now comes the important step – cancel and collect units.If you have chosen the correct conversion factors, you should only be left with the units you want to convert to.
ms
80 km
hr
1 hr
3600 s
1000 m
1 km=
80,000 m
3600 s
A more complex conversionkm to mhr s
Since the unit is correct, wecan now do the math – simplymultiply all the numbers on thetop and bottom, then divide thetwo.
80 km
hr
1 hr
3600 s
1000 m
1 km=
80,000 m
3600 s= 22 m
s
A more complex conversionkm to mhr s
The Answer!!
80 km/hr and 22 m/s are both velocities. A car that is
moving at a velocity of 80 km/hr is traveling the
exact same velocity as a car traveling at 22 m/s.
