Dimensional Analysis Problem Solving

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. 6 10 g 1 Mg 6 _________ _________ 1 Mg = 10 g or 6 1 Mg 10 g 1 Mg –10 _______ ? x Mg = 0.000719 g = 7.19 • 10 Mg x 6 10 g ? How many Megagrams are the same as 0.000719 grams? In other words, convert 0.000719grams to Megagrams. 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

7. 6 -2 10 10 L L 1 M L 1 cL 6 -2 _________ _________ _________ _________ 1 M L = 10 1 c L = 10 L L or or 6 -2 1 M L 1 cL 10 10 L L ? ? cL = 22.6 ML How many Megaliters are the same as 22.6 centiliters? In other words, convert 22.6 centiliters to Megaliters. 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 2.26 EE 9 cL

8. -9 -6 10 10 m m 1 nm 1 m m -9 -6 _________ _________ _________ _________ 1 nm = 10 1 m m = 10 m m or or -6 -9 1 m m 1 nm 10 10 m m ? ? nm = 2260 m m How many nanometer are the same as 2260 micrometers? In other words, convert 2260 micrometers to nanometers. 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 = 2.66 EXP 6 nm

9. -3 -1 10 10 s s 1 ms 1 ds -3 -1 _________ _________ _________ _________ 1 ms = 10 1 ds = 10 s s or or -3 -1 1 ms 1 ds 10 10 s s ? ? ds = 0.75 ms How many deciseconds are the same as 0.75 milliseconds? In other words, convert 0.75 milliseconds to deciseconds. 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 = 7.5 • 10–3 ds

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

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

12. 3 10 454 g g 1 kg 1 lbs 3 _________ _________ _________ _________ 1 kg = 10 1 lbs = 454 g g or or 3 1 lbs 1 kg 10 454 g g ? ? kg = 7.71 x 10-7 lbs How many kilograms are the same as 7.71 x 10-7pounds? In other words, convert 7.71 x 10-7pounds 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 3.50 x 10–7 kg

13. -2 3 10 10 2.54 cm m m 1 m 1 cm 1 inch -2 -1 _________ _________ _________ _________ _________ _________ 1 inch = 2.54 1 dm = 10 1 cm = 10 m cm m or or or 3 -2 1 dm 1 inch 1 cm 10 2.54 10 m cm m ? ? dm = 8.1 x 103 inches How many decimeters are the same as 8.1 x 103inches? In other words, convert 8.1 x 103inches to decimeters. 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 2.1•103 dm

14. 454 g 1 lbs _________ _________ 1 lbs = 454 g or 1 lbs 454 g 454 g _______ ? x g = 136 lbs = 6.17 EE 4 g x 1 lbs g = 136 lbs ? 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. 2. Choose conversion factors that cancels the units we want to discard and leaves the units we want in the result

15. -2 10 0.964 L L 1 cL 1 lbs -2 _________ _________ _________ _________ 1 cL = 10 1 qt = 0.946 L L or or -2 1 qt 1 cL 10 0.946 L cL ? ? cL = 6.70 x 104 qt How many centiliters are the same as 6.70 x 104quarts? In other words, convert 6.70 x 104quarts to centiliters. 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 6.34 EXP 6 cL

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

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