1. Dimensional
Analysis

2. For example, converting 76 centimeters (76 cm) to meters or
Dimensional Analysis is a method for converting from one measurement type to another.
For example, converting 76 centimeters (76 cm) to meters or
76 cm = ? meters

3. 1. The first step is to copy the number with the units.
76 cm
x ________
1 100 m
= 0.76 m cm
2. Multiply the number by a fraction which is called a conversion factor.
3. Whatever the units are on the first measurement, copy those units to the bottom of the conversion factor.
4. In the top part of the conversion factor, put in the units you want to change to.
5. Put in the numbers that relate the two units in the conversion factor.
6. Do the math.

4. Let’s try a similar problem.
34 meters would be how many millimeters? or
34 m = ? mm

5. 1. The first step is to copy the number with the units.
x ________
1000 1 mm
= mm m
2. Multiply the number by a fraction which is called a conversion factor.
3. Whatever the units are on the first measurement copy those units to the bottom of the conversion factor.
4. In the top part of the conversion factor, put in the units you want to change to.
5. Put in the numbers that relate the two units in the conversion factor.
6. Do the math.

6. Let’s do another.
12 kilograms would be how many grams? or
12 kg = ? g

7. 1. The first step is to copy the number with the units.
12 kg
x ________
1000 1 g
= g kg
2. Multiply the number by a fraction which is called a conversion factor.
3. Whatever the units are on the first measurement copy those units to the bottom of the conversion factor.
4. In the top part of the conversion factor, put in the units you want to change to.
5. Put in the numbers that relate the two units in the conversion factor.
6. Do the math.

8. A more difficult problem would be
12 kilograms would be how many milligrams? or
12 kg = ? mg

9. 12 kg
x ________
? ? mg kg
Changing kg to mg in one step is hard so you break the problem up into easier steps.

10. 12 kg x ________ 1000 1 g x ________ 1000 1 mg kg g Instead of kg a mg
Change kg a g then a mg

11. What conversion factor would you use to convert 2
What conversion factor would you use to convert 2.6 liters to milliliters?
1 L
10 mL
A. ______
1 L
100 mL
_______ D.
1000 L
1 mL
_______ B.
100 L
1 mL
_____ E.
1000 mL
1 L
_______ C.

12. What conversion factor would you use to convert 2
What conversion factor would you use to convert 2.6 liters to milliliters?
2.6 L = ? mL
2.6 L x _______ = ? mL
? ?

13. 2.6 L x _______ = ? mL
1000 mL 1 L
? ?
2.6 L
x _______
1000 1 mL
= 2600mL L

14. What conversion factor would you use to convert 2
What conversion factor would you use to convert 2.6 liters to milliliters?
1 L
10 mL
A. ______
1 L
100 mL
_______ D.
1000 L
1 mL
_______ B.
100 L
1 mL
_____ E.
1000 mL
1 L
_______ C.

15. But you’ll need a conversion factor to get from one system to another.
Conversions from one system to another can also be done using dimensional analysis.
But you’ll need a conversion factor to get from one system to another.
Conversions
1.0 meter = 1.1 yard
1.0 liter = 1.06 quarts
1.0 kg = 2.2 pounds (lb)

16. distance
1.0 meter = 1.1 yard
1.0 yard = ? cm
volume
1.0 liter = 1.06 quarts
mass
1.0 kg = 2.2 pounds (lb)
1.0 yd x ________ m
x ______
100 1 cm
= 91 cm yd m

17. American Units of Length
1.0 meter = 1.1 yard
2.0 miles = ? cm ft yd m cm
2.0 miles x _________
5280
x _____ 1
x _____ 1
x ______
100
American Units of Length
Metric Units of Length
mile ft
1.1 yd 1 m 1 3
= 320,000 cm
miles km nm
feet
yards
meters cm
inches mm