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

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.

Writing metric equivalent statements:

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

? 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 ?

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

cL = 22.6 ML _________ or 10 L 1 M L 1 M L = 10 _________ or 10 L 1 cL ? 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. _________ 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

nm = 2260 m m _________ or 10 m 1 m m 1 m m = 10 _________ or 10 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. _________ 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

ds = 0.75 ms _________ or 10 s 1 ms 1 ms = 10 _________ or 10 s 1 ds ? 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. _________ 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

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

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

kg = 7.71 x 10-7 lbs _________ or 454 g 1 lbs 1 lbs = 454 _________ or ? kg = 7.71 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

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

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 = 136 lbs 1 lbs 454 g _______ x ? = 6.17 EE 4 g

cL = 6.70 x 104 qt _________ or 0.964 L 1 qt 1 lbs 0.946 1 qt = 0.946 ? cL = 6.70 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 = 0.946 _________ 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

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

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