Transcript Measurement Conversion and Dimensional Analysis

Measurement
&
I
II
III
Dimensional
Analysis
Learning Objective
 The Learners Will (TLW) express and
manipulate chemical quantities using
scientific conventions and
mathematical procedures such as
measurement conversion and
dimensional analysis
 TEKS 2.G.
Agenda
 Part 3 – Measurement Conversions
Reviewed
A. SI Prefix Conversions –
Shorthand Method
B. Dimensional Analysis –
The “Factor-Label Method” of
solving problems
MEASUREMENT
Unit Conversions
I
II
III
A. SI Prefix Conversions
Move decimal right
move decimal left
Prefix
mega-
Symbol
M
Factor
106
k
103
l,m,g
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
kiloBASE UNIT
A. SI Prefix Conversions
1. Find the absolute difference between
the exponents of the two prefixes
2. Move the decimal that many places
To the left
or right?
If going from larger
factor to smaller,
move decimal to right
If going from smaller
factor to larger, move
decimal to left
A. SI Prefix Conversions
532 m
NUMBER
UNIT
0.532 km
= _______
=
NUMBER
UNIT
A. SI Prefix Conversions
YOUR TURN
1) 20 cm =
0.2
______________
m
32
2) 0.032 L = ______________
mL
3) 45 m =
45,000
______________
nm
0.0805
4) 805 dm = ______________
km
Practice Set
1) 5 cm =
______________ mm
2) 0.006 L = ______________ kL
3) 40 m =
______________ nm
4) 750 m =
______________ km
5) 50,000 g = ______________ kg
B. Dimensional Analysis
 You might not recognize the fancy name,
but you do use it every day
 For example –
 Making change for a dollar bill in dimes
 Converting how many minutes until this
boring class ends into seconds
 Determining how many teaspoons of
medicine to take to equal two tablespoons
B. Dimensional Analysis
 Also called the “Factor-Label” Method
 Units, or “labels” are canceled, or
“factored” out
g
cm 

g
3
cm
3
B. Dimensional Analysis
 Steps:
1. Identify starting & ending numbers and
associated units (labels).
2. Line up conversion factors so units (labels)
cancel. This may mean inverting or
doing the butterfly.
3. Multiply all top numbers & divide by each
bottom number.
4. Check units & answer.
B. Dimensional Analysis
 Step 1:
 What are known factors and units?
 What conversion factors do you have, know, or
need?
 What are you solving for?
You have a belt that is 40 inches long. How long is it in
centimeters?
Starting = 40 inches Ending = x cm
Conversion factor 2.54 cm per inch or 2.54 cm
1 in.
B. Dimensional Analysis
 Step 2: Lining up conversion factors:
1 in = 2.54 cm
=1
2.54 cm 2.54 cm
1 in = 2.54 cm
1=
1 in
1 in
In a word problem,
think of the word “per”
as the fraction line.
If conversion factor is
written as 2.54 cm = 1
in., think of “equals
sign” as fraction line
B. Dimensional Analysis
 Step 3: Multiply all top numbers &
divide by each bottom number
inches
40 inches
cm
2.54 cm
1 in
= 101.6 cm
B. Dimensional Analysis
 Step 4: Check units and answer
 We have cm and our math looks good
B. Dimensional Analysis
 1.How many milliliters are in 1.00 quart
of milk?
qt
mL
1.00 qt

1L
1000 mL
1.057 qt
1L
= 946 mL
B. Dimensional Analysis
 2. 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
B. Dimensional Analysis
 3. 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
B. Dimensional Analysis
4. Your European hairdresser wants to cut
your hair 8.0 cm shorter. How many
inches will he be cutting off?
cm
in
8.0 cm 1 in
2.54 cm
= 3.2 in
B. Dimensional Analysis
5. Industrial’s football team 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
B. Dimensional Analysis
6. A piece of wire is 1.3 m long. How many
1.5-cm pieces can be cut from this wire?
cm
pieces
1.3 m 100 cm
1m
1 piece
1.5 cm
= 86 pieces
B. Dimensional Analysis
 A very useful technique for solving
complex conversion problems,
especially in engineering, chemistry,
physics, medicine
B. Dimensional Analysis
Review the Steps to Using Dimensional
Analysis
More practice as a group and as
individuals – Problem Sets
 Chemistry Textbook – page 95,
problems 15 – 19
 Dimensional Analysis Problem Set