1. Dimensional Analysis Problem Solving
Goals:
under standing what equals, “=“ , means;
the equal sign means “the same as”;
identifying conversion “equivalent” statements used in Factor-Label Method Approach to Dimensional Analysis Problem Solving

2. Factor Label Method supplemental packet page 21
The basic idea is that multiplying a quantity times a fraction
(or several fractions) that equal one does not change the value of
the quantity but may change the units that express the quantity.

3. Writing metric equivalent statements:

4. Lets work out the dimensional analysis problems together supplement packet page 23

5. ?
How many kilograms are the same as 420 grams?
In other words, convert 420 grams to kilograms
1. Begin by writing down conversion factors and their ratios.
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result ?

6. x Mg = 0.000719 g 10 g 1 Mg _______ x = 7.19 • 10 Mg _________ or 10 g?
How many Megagrams are the same as grams?
In other words, convert grams to Megagrams.
1. Begin by writing down conversion factors and their ratios.
_________ or 10 6 g
1 Mg
1 Mg = 10
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result
x Mg = g 10 6 g
1 Mg
_______ x ? =
7.19 • 10
–10 Mg

7. cL = 22.6 ML _________ or 10 L 1 M L 1 M L = 10 _________ or 10 L 1 cL?
cL = ML
How many Megaliters are the same as centiliters?
In other words, convert centiliters to Megaliters.
1. Begin by writing down conversion factors and their ratios.
_________ or 10 6 L
1 M L
1 M L = 10
_________ or 10 -2 L
1 cL
1 c L = 10
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result ?
2.26 EE 9 cL

8. nm = 2260 m m _________ or 10 m 1 m m 1 m m = 10 _________ or 10 m?
nm = m m
How many nanometer are the same as micrometers?
In other words, convert micrometers to nanometers.
1. Begin by writing down conversion factors and their ratios.
_________ or 10 -6 m
1 m m
1 m m = 10
_________ or 10 -9 m
1 nm
1 nm = 10
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result ?
= 2.66 EXP 6 nm

9. ds = 0.75 ms _________ or 10 s 1 ms 1 ms = 10 _________ or 10 s 1 ds?
ds = ms
How many deciseconds are the same as milliseconds?
In other words, convert milliseconds to deciseconds.
1. Begin by writing down conversion factors and their ratios.
_________ or 10 -3 s
1 ms
1 ms = 10
_________ or 10 -1 s
1 ds
1 ds = 10
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result ?
= 7.5 • 10–3 ds

10. Think Metric…or Else! bottom of supplement packet page 22 2.54 0.946
454
Memorize these equivalent statements for
English to Metric conversions

11. Lets work out the dimensional analysis problems together supplement packet page 23

12. kg = 7.71 x 10-7 lbs _________ or 454 g 1 lbs 1 lbs = 454 _________ or?
kg = x 10-7 lbs
How many kilograms are the same as 7.71 x 10-7 pounds?
In other words, convert 7.71 x 10-7 pounds to kilograms.
1. Begin by writing down conversion factors and their ratios.
_________ or
454 g
1 lbs
1 lbs = 454
_________ or 10 3 g
1 kg
1 kg = 10
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result ?
3.50 x 10–7 kg

13. dm = 8.1 x 103 inches _________ or 2.54 cm 1 inch 1 inch = 2.54?
dm = 8.1 x 103 inches
How many decimeters are the same as 8.1 x 103 inches?
In other words, convert 8.1 x 103 inches to decimeters.
1. Begin by writing down conversion factors and their ratios.
_________ or
2.54 cm
1 inch
1 inch = 2.54
_________ or 10 -2 m
1 cm
1 cm = 10
_________ or 10 3 m
1 dm
1 m
1 dm = 10 -1
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result ?
2.1•103 dm

14. g = 136 lbs x g = 136 lbs 1 lbs 454 g _______ x = 6.17 EE 4 g?
How many grams are the same as 136 pounds?
In other words, convert 136 pounds to grams.
1. Begin by writing down conversion factors and their ratios.
_________ or
454 g
1 lbs
1 lbs = 454
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result
x g = lbs 1
lbs
454 g
_______ x ? =
6.17 EE 4 g

15. cL = 6.70 x 104 qt _________ or 0.964 L 1 qt 1 lbs 0.946 1 qt = 0.946?
cL = x 104 qt
How many centiliters are the same as 6.70 x 104 quarts?
In other words, convert 6.70 x 104 quarts to centiliters.
1. Begin by writing down conversion factors and their ratios.
_________ or
0.964 L
1 qt
1 lbs
0.946
1 qt =
_________ or 10 -2 L
1 cL cL
1 cL = 10
2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result ?
6.34 EXP 6 cL

16. Charlie Brown Handout Applying sigfigs and metric conversion 1.6093km
1 mile
10. km x ________ =
6.2 miles
_____
5 min
1 mile
1 hour
60 min
_____
1 hour
12 miles
x ________ =
x __________ = km
1 mile
19 km

17. She is Correct in her statements!!!
Sally and Charlie
She is Correct in her statements!!!
10 mg = 1 cg
10 dg = 1 g
10 • g = 1 •10 -2 g
10 • g = 1 g
m = 10 -3
substitute m for 10 -3
d = 10 -1
substitute d for 10 -1
c = 10 -2
substitute c for 10 -2