1. Dimensional Analysis and Conversion Factors
Sierra Parker CHEM 101

2. Dimensional Analysis
Dimensional analysis is a method that converts one unit to another unit by using conversion factors
Dimensional analysis provides a systematic, straightforward way to set up problems
Very important because being able to setup and solve numerical problems is essential in chemistry

3. Conversion Factors
A numerical ratio used to express a measurement given in one unit as another unit
Ex:
1 min/60 sec quarts/1 gallon in/1ft lb/453.59g
Ex: cm m

4. General Steps
Place the #unit you are converting on the numerator of first fraction
Multiply by correct conversion factor with the same unit in the denominator of next fraction (units should be opposite to each other in the conversion factors so they cross each other out)
Continue step 2 until you end with the unit you are converting to
Cross out all canceled units to make sure you only have the unit you want left
Multiply the top, then multiply the bottom, divide the sum of the top by the sum of the bottom
Write answers with correct units and significant figures

5. Scientific Notation Used for very large or very small numbers
Writing a number as the product of a number between 1 and 10 multiplied by 10 raised to some power

6. Decimal after first nonzero digit
Count how many places the decimal was moved = Exponent
Multiply by 10
The sign of the exponent indicates the direction the decemal was moved
Right = negative (-)
Left = positive (+)

8. Significant Figures (SF)
All nonzero digits
Since all measurements involve uncertainty, it is important to use the correct amount of significant figures
There are 6 rules for significant figures that are important to know

9. Rules Numbers 1-9 are ALWAYS SF (ex. 1,1356=4SF ex. 1356.527=7SF)
0s in front are NEVER SF (ex =2SF ex =3SF)
0s in the middle are ALWAYS SF (ex. 2053=4SF ex =5SF)
0s at the end are ALWAYS SF if there is a decimal point (ex =4SF ex =8SF)
0s at the end are not SF if there is no decimal (ex. 2500=2SF ex. 6760=3SF ex =8SF)
Exact Numbers (Definitions/Some counting) NEVER SF
For multiplying/dividing always use lowest # of SF, for adding/subtracting keep as many SF as the least precise #

10. Back to conversion factors! US/US Conversions

11. Metric/Metric Conversion factors
Meter, Liter, Gram
Ex: 0.01m = 1cm * m/l/g never has the 1 !

12. US/Metric Conversion Factors

13. Multiple Units Conversions

14. Squared/Cubed Conversion factors

15. Word Problem
Ally drives 75 mi/hr to Utah, which is 110 mi always. How long in hours does it take Ally to make it to Utah?