Post on 26-Dec-2015
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Metric and Metric and ConversionsConversions
Mark Ewoldsen, Ph.D.Mark Ewoldsen, Ph.D.
La Cañada High SchoolLa Cañada High School
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
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?
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
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
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!!