Transcript Notes: Math of Physics

V. Units of Measurement
VI. Metric System

Quantity - number + unit
UNITS MATTER!!
Quantity
Symbol
Base Unit
Abbrev.
Length
l
meter
m
Mass
m
kilogram
kg
Time
t
second
s
Temp
T
kelvin
K
Amount
n
mole
mol
Prefix
mega-
Symbol
M
Factor
1x106
1x103
kilo-
k
BASE UNIT
---
deci-
d
1x10-1
centi-
c
1x10-2
milli-
m
1x10-3
micro-

1x10-6
nano-
n
1x10-9

457 dm =

457 dm =
km
mm
1) 20 cm =
0.2
______________
m
32
2) 0.032 L = ______________
mL
3) 45 km =
450,000 dm
______________
0.00805 km
4) 805 cm = ______________
VII. Dimensional Analysis
You will be using these converstions
throughout the year, so its best to take the
time to memorize them now.
1.00 in = 2.54 cm
2.2
lbs = 1.00 kg
1.1
qts = 1.00 L
metric from earlier table

Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom
number hit enter.
4. Check units & answer.

In algebra

In science
ab
What do we do?
b
called factor-label method
◦ Units, or “labels” are canceled, or “factored” out
3
cm
g
g


3
1
cm
Your European hairdresser wants to cut your
hair 8.0 cm shorter. How many inches will he
be cutting off?
Your European hairdresser wants to cut your
hair 8.0 cm shorter. How many inches will he
be cutting off?
8.0 cm 1 in
2.54 cm
= 3.2 in
How many milliliters are in 1.00 quart of milk?

How many milliliters are in 1.00 quart of milk?
qt
1.00 qt
mL
1L
1000 mL
1.057 qt
1L
= 946 mL
Eastview football needs 550 cm for a 1st down.
How many yards is this?
Eastview football needs 550 cm for a 1st down.
How many yards is this?
cm
550 cm
yd
1 in
1 ft 1 yd
2.54 cm 12 in 3 ft
= 6.0 yd
A piece of wire is 1.3 m long. How many
1.5-cm pieces can be cut from this wire?
A piece of wire is 1.3 m long. How many
1.5-cm pieces can be cut from this wire?
m
pieces
1.3 m 100 cm
1m
1 piece
1.5 cm
= 86 pieces

You have 1.5 pounds of gold. Find its volume
in cm3 if the density of gold is 19.3 g/cm3.

You have 1.5 pounds of gold. Find its volume
in cm3 if the density of gold is 19.3 g/cm3.
cm3
lb
1.5 lb 1 kg 1000 g 1 cm3
2.2 lb
1 kg
19.3 g
= 35 cm3
A favorite item at the
fair is bacon on a
stick. If each stick
holds approximately
0.15kg of bacon and
the booth serves an
average of 45 people
an hour, how many
pounds of bacon are
consumed in the 12
days of the fair? (The
gates open at 6:00am
and close at midnight.)



Use the conversion factors you
already know, but when you square or
cube the unit, don’t forget to cube
the number also!
Best way: Square or cube the ENITRE
conversion factor
Example: Convert 4.3 cm3 to mm3
4.3 cm3
(10 mm) 3
(1 cm)
3
=
4.3 cm3
103 mm3
13 cm3
= 4300 mm3
1000 cm3
(1 dm)3
3
=
1
dm
(10 cm)3
So, a dm3 is the same as a Liter !
A cm3 is the same as a milliliter.

How many liters of water would fill a container
that measures 75.0 in3?

How many liters of water would fill a container
that measures 75.0 in3?
in3
L
75.0 in3 (2.54 cm)3
(1 in)3
1L
1000 cm3
= 1.23 L