Transcript C2-Factor-Labeling-or-DA

Factor Labeling or DA
Problem Solving: The easy way!!!
Factor Label Method
Objectives
• How to solve a problems just using units
• How to solve 1 dimension 1 conversion problems
• How to solve 1 dimension –
2 conversion problems
• How to solve multidimensional –
multiconversion problems
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Factor Label Method
• No one method is best for solving
every type of problem
• We Use Dimensional Analysis!!!
• Use the units (dimensions) that are
part of the measurement to help
solve (analyze ) the problem
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How to solve a problems just
using units
A. You must write the following steps in
order to get full credit.
1. Write what you know.
2. Write what you don’t know.
3. Write a plan on how to get from the
known to the unknown.
4. Write the conversion(s) you are going to
use.
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How to solve a problems just
using units
A. You must write the following steps in
order to get full credit.
5. Complete the table
a. Draw a table based on the below:
1 column for known
1 column for each conversion
1 column for the unknown
Every table has 2 rows
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How to solve a problems just
using units
A. You must write the following steps in
order to get full credit.
5. Complete the table
Known_Unit
(Given)
Unknown_Units
Conversion (Answer)
Unknown_Unit
(Answer)
Known_Units
Conversion (Given)
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How to solve a problems just
using units
6. How do you know what goes on top in the
conversion column?
The units you start with go on the bottom.
The units you end with go on the top.
Known_Unit
(Given)
Unknown_Units
Conversion (Answer)
Unknown_Unit
(Answer)
Known_Units
Conversion (Given)
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How to solve a problems just
using units
7. The first column is always what you
start with.
8. The last column is always what you need
to end with.
Known_Unit
(Given)
Unknown_Units
Conversion (Answer)
Unknown_Unit
(Answer)
Known_Units
Conversion (Given)
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How to solve a problems just
using units
9. Notice the red units drop out,
Z*X/Z = X
and you are left with the answer.
Known_Unit
(Given)
Unknown_Units
Conversion (Answer)
Unknown_Unit
(Answer)
Known_Units
Conversion (Given)
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How to solve a problems just
using units
10. IE: How many inches are in X feet?
Known: X feet
?: inches
Plan: feet  inches
Conversion: 1_ft = 12_in
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How to solve a problems just
using units
10: How many inches are in X feet?
Known: X feet
?: inches
Plan: feet  inches
Conversion: 1_ft = 12_in
X feet
12 inches
inches
1 feet
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How to solve a problems just
using units
10: How many inches are in X feet?
The vertical lines mean multiplication
The horizontal lines mean division
Since its either multiplication or division there is
no order of operations!
X feet
12 inches
(X * 12) inches
1 feet
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Sig Fig (Significant Figure) Rules
1. Any number 1-9 is significant
1. 1234 has 4 sig figs
2. 12340000 has 4 sig figs
3. 0123400 has 4 sig figs
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Sig Fig (Significant Figure) Rules
2. Zeros are the problem
1. Zero is not a number but a construct or
idea!
2. Zeros sandwiched between numbers
1.
2.
3.
4.
5.
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101
0101
010100
1.01
0.101
3 sig figs
3 sig figs
3 sig figs
3 sig figs
3 sig figs
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Sig Fig (Significant Figure) Rules
2. Zeros are the problem
1. Zero is not a number but a construct or
idea!
2. Zeros sandwiched between numbers
1.
2.
3.
4.
5.
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101
0101
010100
1.01
0.101
3 sig figs
3 sig figs
3 sig figs
3 sig figs
3 sig figs
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Sig Fig (Significant Figure) Rules
2. Zeros are the problem
3. Decimal Points mess zeros
3. Any zero after a number & before and/or after a
decimal point is significant
1. 1000.
4 sig figs
2. 100.0
4 sig figs
3. 0.1000
4 sig figs
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Sig Fig (Significant Figure) Rules
3. Sig figs in calculations
1. Conversion Factors or constants have
unlimited sig figs so we ignore them
2. If its addition or subtraction
1.
Not really sig figs – least number of digits to
the right of the decimal place wins
1. 15.2 + .002 = 15.2
2. 15.2 – 7
=8
3. If its multiplication or division least number
of sig figs wins
1.
2.
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2.0 * .33333333
5.00/2.5000
= .67 Notice rounding
= 2.00
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Sig Fig (Significant Figure) Rules
3. Sig figs in calculations
4. It goes by last operation performed
1.
So if last operation is + or –
1. Least digits to the right of decimal
2. So if last operation is * or /
1. Least number of sig figs
2. THIS IS WHAT WE USE THE MOST!
5. Rounding
1.
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Find last sig fig – look next door
1. If less than 5, drop everything to right
including it
2. If equal to or greater than five round up 1
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Sig Fig (Significant Figure) Rules
3. Sig figs in calculations
5. Rounding
1.
Find last sig fig – look next door
1. If less than 5, drop everything to right
including it
2. If equal to or greater than five round up 1
2. If need three sig figs
1. 2.333 becomes 2.33
2. 1.009 becomes 1.01
3. 15.9996 becomes 16.0
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How to solve 1 dimension 1 conversion problems
B. How many grams are in 750 centigrams?
Known = 750 centigrams
Unknown = grams
Plan: cg  g
Conversion Factor(s): 100 cg = 1 g
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How to solve 1 dimension 1 conversion problems
B. How many grams are in 750 centigrams?
Known = 750 centigrams
Unknown = grams
Plan: cg  g
Conversion Factor(s): 100 cg = 1 g
750 cg | 1 g | 7.5_g__
| 100 cg |
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How to solve 1 dimension 2 conversion problems
B. How many tons are in 4536 kilograms?
Known = 4536 kilograms
Unknown = tons
Plan: kg  pounds  tons
Conversion Factor(s): .4536_kg = 1_lb, 2000_lb = 1_ton
4536_kg
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1_lb
1_ton
.4536_kg
2000_lb
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5.000_ton
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1 dimension – multiconversions
C. How many seconds are in 5 days?
Known = 5 days
Unknown = seconds
Plan: day  hour  min  sec
Conversion Factor(s): 1 day = 24 hours
1 hour = 60 min
1 min = 60 sec
Solve the problem:
5 days | 24 hrs | 60 min | 60 sec =
| 1 day | 1 hr | 1 min
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432,000_sec = 4.32 X 105 sec
1
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How to solve 2 dimension 2 conversion problems
D. How many km/l are in 12_mi/gal?
1. 2 dimensions – mi to km & gal to liters
Known = 12_mi/gal
Unknown = km/L
Plan: mi/gal  km/L
Conversion Factor(s): 1_mi = 1.609_km & 1 gal = 3.785_L
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How to solve 2 dimension 2 conversion problems
D. How many km/L are in 12_mi/gal?
What is the sig fig answer?
12_mi
gal
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5.1_km/L
1.609_km
1_gal
1_mi
3.785_L
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5.101_km
L
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Deriving Units
• Find the line, square and cube on page 1 of
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•
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C2 DA Packet
Notice the line = 1_m, square = 1_m2 and
the cube = 1_m3
Let 100_cm = 1_m
Now put 100_cm on each edge of square
and solve for how many cm2 in 1_m2
What is 100 cm * 100 cm?
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Deriving Units
• Find the line, square and cube on page 1 of
•
•
•
•
C2 DA Packet
Notice the line = 1_m, square = 1_m2 and
the cube = 1_m3
Let 100_cm = 1_m
Now put 100_cm on each edge of square
and solve for how many cm3 in 1_m3
What is 100 cm * 100 cm * 100 cm?
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Final Thoughts
• That last technique works for anything unit
that starts with a length.
• You must use the conversions on the sheet
• Your homework is the C2 DA Packet
• Its due the next class meeting
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