Why is dimensional analysis useful?

Answer 1

Answer 2

Here's an example of dimensional analysis' usefulness outside the world of science and outside the world of school:

You take a trip to Toronto having lived in the United States all your life. Canada, like most countries, uses the metric system (km., m), not the Imperial system (miles, yards). All of the speed limit signs in Canada are in km/hr., but your American car is in mi/hr. To convert 90 km/hr. to mi/hr:

90 km./hr. * 0.62 mi./1 km.= 55.8 mph

Dimensional analysis can help you avoid speeding tickets. If you read as miles, you will exceed the actual speed limit by about 35 mph!

Answer 3

Whereas the answer provided by @Andrew L is quite useful, there are other reasons why we want to understand how to use dimensional analysis (DA), and more specifically related to Chemistry, as opposed to physics.

Many students, when first beginning Chemistry, have difficulty answering questions that have some type of math (arithmetic) involved. If you understand DA, sometimes you don't even need to understand the question in order to get the answer, if you just understand DA. To use the method effectively, you begin with what you are given, and then use appropriate UNITS to get what you want.

For example, if you are asked "how many moles of iron (Fe) are in 445 grams of Fe, even if you don't completely understand the concepts, you can arrive at a correct answer as follows:

Begin with what is given, i.e. 445 g Fe. Then use appropriate units (DA) to convert to moles, knowing that there are 55.85 g Fe in 1 mole of Fe (see the periodic table for this conversion factor):

445 g Fe x 1 mole Fe = 7.97 moles Fe (ANSWER)

55.85 g Fe

In the above DA, note how the g Fe cancel leaving you with moles of Fe, which is what the question asked for.