Metric and
Conversions
Mark Ewoldsen, Ph.D.
La Cañada High School
Units
and
Measurement
Physics
Mrs. Coyle
http://apod.nasa.gov/apod/image/0706/iss_sts117_big.jpg
Countries that do NOT use Metric
Basic Physics – SI Units
Quantity
Unit
Symbol
Length
meter
m
Mass
gram
g
Time
second
S
Volume
liter
L
SI Unit Prefixes- Part II
Name
Symbol
Factor
giga-
G
109
mega-
M
106
kilo-
K
103
centi-
c
10-2
milli-
m
10-3
micro-
μ
10-6
SI Unit Prefixes for Length
Name
Symbol
gigameter
Gm
109
megameter Mm
106
kilometer
Km
103
meter
m
100
centimeter
cm
10-2
millimeter
mm
10-3
micrometer
μm
10-6
nanometer
nm
10-9
picometer
pm
10-12
1000 Mm
1000 km
1000 m
1000 mm
.01 m
1000 μm
1000 nm
1000 pm
Scientific Notation
Mx
n
10
or
M 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 will have a
negative exponent.
A millionth of a second is:
0.000001 sec
1.0E-6
1x10-6
Solving Word Problems
• Analyze
– List knowns and unknowns.
– Draw a diagram.
– Devise a plan.
– Write the math equation to be used.
• Calculate
– If needed, rearrange the equation to solve for the
unknown.
– Substitute the knowns with units in the equation and
express the answer with units.
• Evaluate
– Is the answer reasonable?
How to Convert Units
Made Easy
Converting
10 inches to centimeters
10.0 in
= cm
We start by writing down the
units of what we want and then
number and the units given
Our conversion factor for this is
1 in = 2.54 cm.
Then
2.54 cm
=
1 in
1
Multiplying by 1 does not change the value!
Converting
Inches to centimeters
10.0 in
=
cm
Our conversion factor for this is 1 in = 2.54 cm.
Converting
Inches to centimeters
10.0 in 2.54 cm =
1 in
cm
Our conversion factor for this is 1 in = 2.54 cm.
Since we want to convert to cm, cm goes on the
top.
Converting
Inches to centimeters
10.0 in 2.54 cm =
1 in
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
Converting
Inches to centimeters
10.0 in 2.54 cm = cm
1 in
Leaving us with cm – the unit we want.
Converting
Inches to centimeters
10.0 in 2.54 cm = 25.4 cm
1 in
Since the unit is correct,
all that is left to
do is the arithmetic...
The
Answer
A more complex conversion
km to m
hr
s
A more complex conversion
km to m
hr
s
80 km
hr
Step 1 –
Write down the
number and the
unit!
A more complex conversion
km to m
hr
s
80 km
1 hr
hr 3600 s
m
=
s
First we’ll convert time. Our conversion factor is
1 hour = 3600 sec. Since we want hours to cancel
out, we put it on the top.
A more complex conversion
km to m
hr
s
80 km
1 hr
1000 m
hr 3600 s 1 km
m
=
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.
A more complex conversion
km to m
hr
s
80 km
1 hr
1000 m
hr 3600 s 1 km
m
=
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.
A more complex conversion
km to m
hr
s
80 km
1 hr
1000 m
=
hr 3600 s 1 km
80,000 m
3600 s
Since the unit is correct, we
can now do the math – simply
multiply all the numbers on the
top and bottom, then divide the
two.
A more complex conversion
km to m
hr
s
80 km
1 hr
1000 m
=
hr 3600 s 1 km
80,000 m
m
= 22 s
3600 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.