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
kilogram
kg
Time
second
S
Volume
liter
L
SI Unit Prefixes - Part I
Name
Symbol
Factor
tera-
T
1012
giga-
G
109
mega-
M
106
kilo-
k
103
SI Unit Prefixes- Part II
Name
Symbol
Factor
centi-
c
10-2
milli-
m
10-3
micro-
μ
10-6
nano-
n
10-9
pico-
p
10-12
femto-
f
10-15
Derived SI Units (examples)
Quantity
Unit
Symbol
Speed
meter per second
m/s
Newton
kg m/ s2
N
Energy
Joule (kg m2/s2)
J
Pressure
Pascal (kg/(ms2)
Pa
SI Unit Prefixes for Length
Name
Symbol
gigameter
Gm
109
megameter Mm
106
kilometer
km
103
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 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:
5.45E+6
or
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?
Unit
Conversions
Dr. John Mattox
Department of Chemistry and Physics
Fayetteville State University
1200 Murchison Rd.
Fayetteville, NC 28301
How to Convert Units
Made Easy
Converting
10 inches to centimeters
10.0 in
= cm
We start by writing down the
number and the units given
and units of what we want
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
Even though we have two different numbers
and two different units, they represent the
exact same length. You can check this by
looking at a ruler – find the 10 in mark and
directly across at the cm side. What number
do you find?
A more complex conversion
km to m
hr
s
In order to work a NSCI 110 homework
problem, we need to convert kilometers
per hour into meters per second. We
can do both conversions at once using
the same method as in the previous
conversion.
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.