1. Using units to solve problems
Dimensional Analysis
Using units to solve problems
2.5 m X 1km = km
1000 m
Conversion Factor – Used to change from one unit to another.
Top equals the bottom
Conversion factors = 1

2. Example How many seconds are in 3 hours? s min hr (X) (3)
3hr X 60 min X 60 s = 10,800 s
1 hr min

3. Procedure Write down each unit in the problem once.
Draw lines to show conversion factors.
Use units to set up problems.
Put in numbers and solve.

4. Practice
Convert 10 cm to km
cm m km

5. Convert 10 cm to km
10 cm X 1 m X 1km = 100 cm 1000 m 10 cm = km

6. How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x min = min
1 hr
cancel
By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

7. Sample Problem
You have $7.25 in your pocket in quarters. How many quarters do you have?
7.25 dollars quarters
1 dollar
= 29 quarters X

8. You Try This One!
If Jacob stands on Spencer’s shoulders, they are two and a half yards high. How many feet is that?

9. Learning Check a) 2440 cm b) 244 cm c) 24.4 cm
A rattlesnake is 2.44 m long. How long is the snake in cm?
a) cm
b) 244 cm
c) 24.4 cm

10. Solution
A rattlesnake is 2.44 m long. How long is the snake in cm?
b) 244 cm
2.44 m x cm = 244 cm
1 m

11. How many seconds are in 1.4 days? Unit plan: days hr min seconds
Learning Check
How many seconds are in 1.4 days?
Unit plan: days hr min seconds
1.4 days x 24 hr x ??
1 day

12. How many gits equal 5 hews?
20 gits equal 1 erb
1 futz equals 2 hews
10 erbs equal 1 futz

13. How many drams is 4.0 grams?
1 pound = 7000 grains
16 ounces = 1 pound
3 scruples = 1 dram
454 grams = 1 pound
30 grams = 1 scruple

14. A blacksmith has to put new shoes on a stable of 20 horses
A blacksmith has to put new shoes on a stable of 20 horses. Each shoe requires 3 nails. How can he or she calculate the number of nails that must be brought to the stable?