DERIVED
UNITS
Combining measurements
to describe physical
properties
DERIVED UNIT
 Derived
units are created from combining
other base units
 Examples:
Volume:
the amount of
space an object takes up
Density: how much mass
is in a certain volume
VOLUME
 Volume
formula:

is derived by taking the following
Volume = l x w x h
 To
solve, you do the same things to the
units as you do to the numbers
 If you have a box 10cm x 10cm x 10cm:
 Volume = 10cm x 10cm x 10cm
 Volume = 1000 cm3
 The derived unit is cm3
NOTE
1
This
3
cm
= 1 mL
is an important
conversion. Make sure it is
easily found in your notes
 For example: 25cm3 = 25mL
DENSITY
 Density
is the ratio of mass to volume
 Mathematically this is expressed as
follows:


Density = mass
volume
Each variable is abbreviated
D = density
 m = mass
 V = volume

DENSITY
 The density
 D=m
V
 Again,
formula is summarized as:
the units are also divided by
each other
 Below are some examples of density
units:



g/cm3
g/mL
kg/m3
EXAMPLE

An object has a mass of 15.0g and a
volume of 5.0mL. What is the density?

NOTE: I am much more interested in the
unit than the number answer
SOLUTION
D
= M/V
D
= (15.0g)/(5.0mL)
D
= 3g/mL
 NOTE:
In addition to dividing the number,
you also divide the units
TRY THESE
A
car travels 200km in 4 hours, calculate
the speed.
 A student at college buys 8 books. His
total price is $160. What is the price per
book?
 A bullet covers 5000m in 2 seconds,
calculate the speed.
USING DENSITY TO SOLVE FOR
MASS AND VOLUME
You
can also solve for mass
and volume.
Normally, you would use
algebra
We are going to use a
technique called dimensional
analysis
TITLE: FLAME TEST LAB


1.
2.
3.
4.
5.
Purpose: To determine an unknown
substance using a flame test.
Procedure:
Insert flame loop into a chemical
sample.
Make all of your observations about the
flame.
Repeat for each of your known
chemicals.
Insert flame loop into unknown sample.
Determine the unknown.
DIMENSIONAL ANALYSIS
 Another
way to solve problems is using a
process called dimensional analysis
 You will be solving density problems using
dimensional analysis
 Dimensional analysis: method of solving
problems where the units cancel out
EXAMPLE


If a block has a density of 25kg/L and a
volume of 10L, what is the mass?
For dimensional analysis, you need to be
able to cancel out units until the one you
are solving for is left
Step 1: You always begin with the known value
that has 1 UNIT after the number.
 NOTE: 10L only has liters (L) after the
number
 Therefore, you start the problem with 10L
EXAMPLE
Step 2: Find the conversion in the problem.
The conversion is the number that has 2
units after the number.

NOTE: 25 kg/L has two units after
the number, both kilograms (kg)
and liters (L)
Step 3: Put the two values together in a “T
chart” so that 2 of the units cancel and you
are left with 1 unit.
DIMENSIONAL ANALYSIS
 Step
1:
Write your known starting value
 10L
 Step 2: Set up a T chart to cancel out
units using the conversion (density)
 10L
| 25kg_
| 1L
 Step 3: Cancel out the units to solve (for
mass)
 10L
| 25kg_
= 250kg
| 1L
TRY THIS OUT
A
block has a density of
15g/mL. If the block has a
mass of 5g, what is the
volume?
 NOTE: When you set it up, you will want
to cancel grams (g)
TRY ONE OUT
A
block has a density of
10g/mL. If the block has a
mass of 0.025 kg, what is the
volume?
HINT:
To cancel out units,
they must be the SAME unit.
ANSWER
D
= 10g/mL
M = 0.025kg = 25g
(convert unit)
V= ?
25 g | 1mL = 2.5 mL
| 10 g
USING DIMENSIONAL
ANALYSIS IN METRIC
 Before,
we looked at using ratios to solve
for metric conversions.

Now we will use dimensional analysis.
 The
steps are the same, the only
difference is we use the 2 units from the
chart to convert.
 REMINDER:


Step 1: Convert to the base unit first
Step 2: Convert to the second unit next
EXAMPLE
 Convert:
250mm = ??? hm
 First,
find the metric conversions on your
sheet


1m = 1000mm
1hm = 100m
 Second,
take your starting value (250mm)
and convert it to the base unit
CONVERT TO BASE UNIT
250mm | 1m_____ = 0.25m
| 1000mm
 NOTE:
You put the mm on the
bottom to cancel out the 250 mm
on top
 Since the 1000mm is on the bottom,
you divide
CONVERT TO SECOND UNIT
0.25m | 1hm_____ = 0.0025hm
| 100m
 NOTE:
You use the answer from the
first step in the second step
 Since the 100m is on the bottom,
you divide
TRY THESE
Convert
units
225mg
the following metric
=
33.4cm
=
4.56x1010nL =
______g
______hm
______ cL
HOW DO YOU DETERMINE
SIG. FIGS. IN DERIVED UNITS
 When
multiplying or dividing, you
find the number with the fewest
number of sig. figs.
 This is the number of sig. figs. in your
answer
 Example: 3.024 x 2.11 = 6.38064
(4 sig. figs.) (3 sig. figs.)
Change to correct sig. fig.= 6.38
(Fewest sig. figs. is 3)
TRY THE FOLLOWING
1.
2.2500 x 2500 =
2.
2.04 x 10-3 x 8.808 x 102 =
3.
4.05 x 105 =
3.625 x 102
ANSWER

2.2500 x 2500 = 5.6 X 103 (2 sig. figs.)

2.04 x 10-3 x 8.808 x 102 = 1.80 (3 sig. figs.)


4.05 x 105 = 1.12 x 103 (3 sig. figs.)
3.625 x 102
NOTE: You must round correctly, when
doing significant figures
PROBLEM #1
 Solve
using significant figures:
______(367.21)*(24.783)_____
(19.5623)*(5.987218)*(521.931)
PROBLEM #2
An
object has a mass of
2.25x103 mg and a density of
5.0g/mL. What is the volume?