1. Dimensional Analysis

2. What is Dimensional Analysis?
Dimensional analysis is a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value.
It is used to go from one unit to another.
A conversion factor, or a fraction that is equal to one, is used, along with what you’re given, to determine what the new unit will be.

3. Conversion Factors Examples
Equality seconds = 1 minute
Conversion factors: s or 1 min
1 min s
Equality- 60 min = 1 hr
Conversion factors: min or 1 hr
1 hr min
Any others?

4. Calculate the number of minutes in 3.61 hours.
Dimensional Analysis
Calculate the number of minutes in 3.61 hours.
*Note: Use the number given in the question to determine the number of sig figs in your answer.
1. Write the given.
2. Draw the chart.

5. 3. Think of a relationship: 1 hr = 60 min 4. Cancel units diagonally.
Dimensional Analysis
Calculate the number of minutes in 3.61 hours.
*Note: Use the number given in the question to determine the number of sig figs in your answer.
3. Think of a relationship: 1 hr = 60 min
4. Cancel units diagonally.

6. 5. Add the rest of the relationship.
Dimensional Analysis
Calculate the number of minutes in 3.61 hours.
5. Add the rest of the relationship.
Multiply across and divide by the bottom
Count sig figs in the given. Round
the answer to that number of sig figs.

7. Conversion Factor: 1 in= 2.54 cm
Dimensional Analysis
How many centimeters are in 4.2 inches?
*Note: Use the number given in the question to determine the number of sig figs in your answer.
Conversion Factor: 1 in= 2.54 cm

8. How many centimeters are in 4.2 inches?
Dimensional Analysis
How many centimeters are in 4.2 inches?
*Note: Use the number given in the question to determine the number of sig figs in your answer.

9. Realize that we don’t know just one step from weeks to seconds.
Dimensional Analysis
Multi-Step Problems
Calculate the number of seconds in two weeks.
Realize that we don’t know
just one step from weeks to seconds.

10. Dimensional Analysis Multi-Step Problems Start as usual.
Calculate the number of seconds in two weeks.
Start as usual.

11. Dimensional Analysis Multi-Step Problems Extend your table.
Calculate the number of seconds in two weeks.
Extend your table.

12. Continue adding relationships.
Dimensional Analysis
Multi-Step Problems
Calculate the number of seconds in two weeks.
Continue adding relationships.

13. Add as many conversions as needed.
Dimensional Analysis
Multi-Step Problems
Calculate the number of seconds in two weeks.
Round to 1 sig fig.
Add as many conversions as needed.

14. Notice the use of the bottom space.
Dimensional Analysis
Multi-Step Problems
Convert the density of 0.58 g/mL to lb/gallon (1 L = qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Notice the use of the bottom space.

15. Ignore the bottom unit for a moment.
Dimensional Analysis
Multi-Step Problems
Convert the density of 0.58 g/mL to lb/gallon (1 L = qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Ignore the bottom unit for a moment.
Concentrate on converting the top unit.

16. Continue converting the top. Stop when you get to lb…the goal.
Dimensional Analysis
Multi-Step Problems
Convert the density of 0.58 g/mL to lb/gallon (1 L = qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Continue converting the top.
Stop when you get to lb…the goal.

17. Now, focus on the bottom units.
Dimensional Analysis
Multi-Step Problems
Convert the density of 0.58 g/mL to lb/gallon (1 L = qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Now, focus on the bottom units.
It is OK to cancel units from a distance.

18. Continue adding until you reach the goal.
Dimensional Analysis
Multi-Step Problems
Convert the density of 0.58 g/mL to lb/gallon (1 L = qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Continue adding until you reach the goal.

19. If a pound of apples costs $0.79, then 5.3 lbs will cost _________.
Fill-In
iRespond Question
If a pound of apples costs $0.79, then 5.3 lbs will cost _________.
Give your answer to TWO decimal places which is customary with money.
A.) 4.19;;
B.)
C.)
D.)
E.)

20. 1849 yards = __________ miles Hint: 5280 ft = 1 mile
Fill-In
iRespond Question
1849 yards = __________ miles
Hint: 5280 ft = 1 mile
Give your answer to 4 sig figs.
A.) 1.051;;
B.)
C.)
D.)
E.)

21. Give your answer to TWO sig figs.
Fill-In
iRespond Question
If Boston and New York City are 190 miles apart, then the distance between the two cities is _______ km.
Hint: 1 km = miles
Give your answer to TWO sig figs.
A.) 310;;
B.)
C.)
D.)
E.)

22. Give your answer to THREE sig figs.
Fill-In
iRespond Question
If a pound of apples costs $0.79, then a shopper with $2.00 will be able to purchase ________ lbs of apples.
Give your answer to THREE sig figs.
A.) 2.53;;
B.)
C.)
D.)
E.)

23. F
Fill-In
iRespond Question
If a US car advertisement brags that an SVU gets 26 miles/gallon on the highway, then the same car would be described in Europe as getting ___________ km/L.
Hint: 1 L = qt; 4 qt = 1 gal; km = miles
Give your answer to TWO sig figs.
A.) 11;;
B.)
C.)
D.)
E.)