1. The SMART way FACTOR-LABEL (aka DIMENSIONAL ANALYSIS)
PROBLEM-SOLVING
The SMART way
FACTOR-LABEL
(aka DIMENSIONAL ANALYSIS)

2. When the values are familiar, it is easy.
We convert all the time.
When the values are familiar, it is easy.
When the problem is short it is simple.
But in chem, you will need to solve problems that are neither familiar nor short!

3. Factor-Label
Use CONVERSION FACTORS
LABEL all units
The labels on the factors guide you through the problem as they cancel out

4. Factor-label to the rescue!
Here I come to save the day!

5. Factor-Label Method Use for conversion problems
Changing from one unit to another
Only use for multiplication and division problems

6. Equalities Equalities Two ways to express the same thing
The quantities are equal, but they are expressed in different units
EX: 1” = cm
7 days = 1 week

7. Equalities
If the 2 equal quantities are divided, the answer is 1…you get unity.
If you divide a value by itself, you get 1
So we get CONVERSION FACTORS from
1” = 2.54 cm days = 1 week
1” = cm = 1
2.54 cm ”
7 days = 1 week = 1
1 week days

8. Write down the starting factor and units. EX: How many cm in 1.98 m?
HOW TO DO FACTOR-LABEL CONVERSION PROBLEMS
Write down the starting factor and units.
EX: How many cm in 1.98 m?
Give yourself room on the paper to work and go to the end and write the desired unit or final factor
EX: m = cm

9. Use the appropriate conversion factor(s) (from equalities) to cancel unwanted units and leave desired units. Any label on both top and bottom of the fractions cancels.
EX: Equality m = 100 cm
This yields two conversion factors
1 m or cm =
100 cm m

10. Cancel the UNITS ONLY that are on the top and bottom of the fractions.
EX: Equality m = 100 cm
this yields two conversion factors m or cm =
100 cm m
Which one to use?
Set up the problems with the one that results in the cancellation of the starting unit.
1.98 m | cm = cm
1 m
Cancel the UNITS ONLY that are on the top and bottom of the fractions.

11. Do the math to solve.
Multiply by all values on the top
Divide by all values on the bottom
Write the answer with units and the correct number of sigdigs
Note: Counted values and defined conversion factors do not limit sigdigs…only measured values.
Why? Sigdigs convey the precision of a measurement. We can count exactly and we define certain values exactly.
EX: m | cm = cm
| m

12. Note: with this “picket fence” set up, the vertical bars separate fractions
1.98 m | cm = cm
| m
Is the same as
1.98 m X cm = cm
1 m
You may set yours up either way, but many students find it easier to keep long problems organized with the picket fence style.

13. How many SCHNIZZLES in 12 TWIZZLES?
What do you know? Starting factor
What do you want to know? Final factor
Start: Twizzles
Desired/Final: ______ Schnizzles
How do you get from the START to FINAL?
You need to find or know some EQUALITIES to use as CONVERSION FACTORS
10 Sizzles = 5 Fizzles
1 Frizzle = 3 Sizzles
18 Fizzles = 1 Twizzle
2 Frizzles = 5 Schnizzles
These are defined and counted conversion factors. Report all digits as significant.
Start TwizzlesConversion Factors   Final Schnizzles

14. It will guide you through lots chemistry problems, too!
Congratulations!
Factor-Label has guided you through a problem that you knew nothing about!
It will guide you through lots chemistry problems, too!

15. A familiar example