1. Bellringer How many pounds do you weigh? How many ounces?
How did you arrive at that figure?

2. Dimensional Analysis aka Factor Label Method aka Conversion Factors
Ms. Hanlon’s
Science Classes

3. Objectives
Correctly set up word problems and cancel units to solve dimensional analysis problems.

4. Definition
Dimensional Analysis: checking a derived equation by making sure dimensions are the same on both sides.
Units, or “labels” are canceled, or “factored” out

5. Steps 1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.

6. Conversion Factors
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units but always equal to one. You can always multiply any equation by this equality and not change the quantity, just the units.
Example: in. = 2.54 cm
Factors: 1in and cm
2.54 cm in.

7. First write down the desired quantity
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
First write down the desired quantity

8. Next, equate desired quantity to the given quantity
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
Next, equate desired quantity to the given quantity

9. Now we have to choose a conversion factor
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
Now we have to choose a conversion factor

10. What conversion factors are possible?
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
1 km
0.621 mi
0.621 mi
1 km
What conversion factors are possible?

11. Pick the one that will allow you to cancel out miles
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will allow you to cancel out miles

12. Pick the one that will allow you to cancel out miles
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will allow you to cancel out miles

13. Multiply given quantity by chosen conversion factor
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
1 km
0.621 mi
0.621 mi
1 km
Multiply given quantity by chosen conversion factor

14. Multiply given quantity by chosen conversion factor
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
x 1 km
0.621 mi
Multiply given quantity by chosen conversion factor

15. Cross out common factors
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
x 1 km
0.621 mi
Cross out common factors

16. Cross out common factors
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
x 1 km
0.621
# km
= 47.0
Cross out common factors

17. Are the units now correct?
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
x 1 km
0.621
# km
= 47.0
Are the units now correct?
Yes – km on both sides!

18. Factor label Example Now finish the math.
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= 47.0
x 1 km
0.621
= km
Now finish the math.

19. Not Finished Yet Complete the math with no rounding
Make certain the sig figs are correct by rounding to the correct number of sig figs at the very end
Don’t forget the order of operations when you complete the math
Conversion factors do not determine sig. figs.!

20. Factor label Example The final answer is 75.7 km
How many kilometers are in 47.0 miles? (note: 1 km = miles)
x 1 km
0.621
= 75.7 km
# km
= 47.0
The final answer is 75.7 km

21. Classwork Get into groups as assigned.
Rotate among stations and complete lab activities.

22. Homework
Complete the worksheet provided.