How to get Unit Conversions Right Every Time, with Tricky Multi-step Examples

This video tutorial shows how to do unit conversions in a simple, systematic way so you can get them right every time. The method is demonstrated with simple and multi-step unit conversions, including one with multiple units that must be converted at the same time.

Many thanks to Greg Schwanbeck, who in September 2009 posted a fantastic YouTube video about unit conversions. To see Greg’s video, check out this link: https://www.youtube.com/watch?v=XKCZn5MLKvk.

—

Transcript:

Hey! I’m Scott, from RedmondPhysicsTutoring.com, and this video will help you master unit conversions.

I’ll start with a single-step conversion. The amount I start with goes on the left, and what I get goes on the right. In the middle, I multiply by a conversion factor with the top and bottom equal (these are in green). I divide by the units I have (in red), so they cancel out, and multiply by the units I want (in blue) so they show up on the right. Here’s a quick example, converting 60 lbs to Newtons. 1 lb = 4.45 N, and I want to cancel out the lbs so for the conversion factor I put 1 lb on the bottom, then 4.45 N on top. 60 x 4.45 = 267, so 60 lbs is equal to 267 Newtons.

That’s pretty simple. How about a multistep problem like converting 19 m to inches? Just chain the conversion factors together. I can look up the conversion factors: 1 m = 100 cm, 1 ft = 12 in, and 1 in = 2.54 cm. If you’re not sure what to use, just write them down and link them together visually on paper. I’m starting with m, and I want inches. I can go from m to cm, then from cm to inches. Nice!

I put 19 m on the left, and I want to get rid of m so I put m on the bottom of the conversion factor, and then cm on the top. Then I’ll go from cm to inches, so I put 2.54 cm on the bottom of the next conversion factor and 1 inch on the top. Finally, I multiply it out: 19 x 100 / 2.54 = 748, so 19 m = 748 inches.

Now how about multiple units? In Back to the Future, the DeLorean has a takeoff speed of 88 mph. How fast is that in m/s? Now we have to convert miles to meters and hours to seconds. I’ll start with miles: 1 mile = 5280 feet, 1 ft = 12 in, 1 in = 2.54 cm, 100 cm = 1 m. Then I’ll do hours: 1 h = 60 min and 1 min = 60 s. Notice that I start with miles and hours, and end with meters and seconds, which is what we want.

I put 88 miles over 1 h on the left, and then start filling in the conversion factors. I put miles on the bottom to cancel it out, with feet on top. Then feet on the bottom for the next one, and inches on top. Then inches on the bottom and cm on top, then cm on the bottom and meters on top. That converts miles to m, but I still need to convert hours to s. The hours were originally on the bottom, so I need to put them on the top – in the conversion factor – to cancel them out. I also need to put minutes on the bottom here, and then minutes on top and seconds on the bottom for the last conversion factor. This all works out to 88 x 5280 x 12 x 2.54 / 100 / 60 / 60 and gives 39.3 m/s. Done.

If you prefer, you can do it one step at a time. It takes longer to write, but you’re less likely to make a mistake.

I really hope this helps you out! If so, please like this video to let me know. Good luck!

via YouTube http://youtu.be/1XTbJ4F1V-c