i ii iii measurement & dimensional analysis. learning objective the learners will (tlw) express...
TRANSCRIPT
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
A. SI Prefix Conversions
mega- M 106
deci- d 10-1
centi- c 10-2
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
nano- n 10-9
pico- p 10-12
kilo- k 103
mo
ve d
ecim
al le
ft
Mo
ve d
ecim
al r
igh
t
BASE UNIT l,m,g 100
Scientific Notation
is Back!!!!!!!!
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 leftor 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
YOUR TURN
1) 20 cm = ______________ m
2) 0.032 L = ______________ mL
3) 45 m = ______________ nm
4) 805 dm = ______________ km
0.2
0.0805
45,000
32
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
3
3
cm
gcm
B. Dimensional Analysis
Also called the “Factor-Label” Method Units, or “labels” are canceled, or
“factored” out
g
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
2.54 cm 2.54 cm
1 in = 2.54 cm
1 in 1 in
= 1
1 =
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 cm
40 inches 2.54 cm
1 in= 101.6 cm
B. Dimensional Analysis
1.How many milliliters are in 1.00 quart of milk?
1.00 qt 1 L
1.057 qt= 946 mL
qt mL
1000 mL
1 L
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.
lb cm3
1.5 lb 1 kg
2.2 lb= 35 cm3
1000 g
1 kg
1 cm3
19.3 g
B. Dimensional Analysis
3. How many liters of water would fill a container that measures 75.0 in3?
75.0 in3 (2.54 cm)3
(1 in)3= 1.23 L
in3 L
1 L
1000 cm3
B. Dimensional Analysis
4. 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
cm in
B. Dimensional Analysis
5. Industrial’s football team needs 550 cm for a 1st down. How many yards is this?
550 cm 1 in
2.54 cm= 6.0 yd
cm yd
1 ft
12 in
1 yd
3 ft
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?
1.3 m 100 cm
1 m= 86 pieces
cm pieces
1 piece
1.5 cm
B. Dimensional Analysis
A very useful technique for solving complex conversion problems, especially in engineering, chemistry, physics, medicine