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Homework Tips For Conversions

01/09/2013 1:23 PM

Although we don't do homework here, I thought it would be nice to offer a tip that was very useful. Frequently the point in which students become bogged down is nothing more than getting some answer into the terms that is required. This technique is rather obvious to some, but it couldn't be any more straight forward.

When you have something like a rate of change of something in one set of parameters and you wish to convert it to another set of parameters the first step will be thinking of the rate as a fraction. So, if you take some rate such as:

X gallons/minute and you want to convert it to Y liters/second

On the left (above) is :

X

gallons
minute

Where the magnitude of the rate is X, the terms are gallons (in the numerator) and minute(s) in the denominator. Any step you need to use simply lists the conversion factor in the same way. So to convert you set it up like this:

X

gallons

3.785 Liters

minute

minute

gallon

60 seconds

Note that the number 3.785 is the magnitude of Liters per Gallon, and 60 is the number of seconds per minute. The word "per" is the clue to draw your horizontal line to seperate the numerator from the denominator.

Next, since like terms cancel, you can draw a line through both sets of terms "gallons" and "seconds" leaving only:

The magnitude is X times 3.785 divided by 60

and the left over terms verify that you ended up where you wanted. That is to say that the left over terms (the ones that did not cancel) are Liters per second.

I still remember how easy this became when I first treated it like multiplying fractions together. And it checks your work by looking at the remaining terms. Good Luck and no, we don't do homework problems.

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#1

Re: Homework Tips for conversions

01/09/2013 1:26 PM

Thanks Joe. I always wondered how to do that.

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#3
In reply to #1

Re: Homework Tips for conversions

01/09/2013 3:28 PM

Do I sense some sarcasm?

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#4
In reply to #3

Re: Homework Tips for conversions

01/09/2013 6:25 PM

What a terrible thing to think. Those tips are the most sensible and lucid stuff I've read in...oh, never mind. I haven't looked at the fracking thread in at least 10 minutes.

'Percent' derives from the latin for 'cat urine', possibly.

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#2

Re: Homework Tips For Conversions

01/09/2013 1:50 PM

I think the buzz words for this are "Factor Label Method".

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#5
In reply to #2

Re: Homework Tips For Conversions

01/09/2013 8:06 PM

Oh? On second glance [not that a second glance was actually necessary, mind you] I was under the impression the official term is "I think I'll go paint my nails now." My bad.

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#15
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Re: Homework Tips For Conversions

01/10/2013 1:22 PM
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#6

Re: Homework Tips For Conversions

01/09/2013 11:52 PM

so thats US gallons to litres not british standard gallons 4.54609 to litres

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#8
In reply to #6

Re: Homework Tips For Conversions

01/10/2013 4:02 AM

Isn't the Atlantic Ocean wonderful?

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#9
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Re: Homework Tips For Conversions

01/10/2013 7:24 AM

Yeah but just wait til you cross the English Channel! :))))

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#7

Re: Homework Tips For Conversions

01/10/2013 12:26 AM
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#10

Re: Homework Tips For Conversions

01/10/2013 8:49 AM
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#11

Re: Homework Tips For Conversions

01/10/2013 10:02 AM

I've been doing that for years. Personally I call it dimensional analysis. Works great, and you can go thru several steps to get where you need to go.

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#12

Re: Homework Tips For Conversions

01/10/2013 10:02 AM

This is called Dimensional Analysis and I seriously believe it is the one best thing I learned in all of High School. Thanks to my chemistry teacher.

It's really one of those common sense things which isn't nearly common enough.

(edit: I see "Dimensional Analysis" has been mentioned already. +1 for them!)

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#13

Re: Homework Tips For Conversions

01/10/2013 12:15 PM

Over the decades, I have found many who have forgotten or neglect to use this simple technique. One of the most common real world uses is I have had for this is to show engineers who now wear management hats that the result they derived was obtained using the wrong assumptions and, therefore, the wrong equations. This is easily done when the equation used cannot deliver the dimensions required for the answer.

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#14

Re: Homework Tips For Conversions

01/10/2013 12:22 PM

Thank you for the excellent tip. It leads the person through a logical progression to get the answer instead of using those multiplication or division factors that teach nothing. Remembering just a few conversions (metric to English, ounces to pounds, gallons to liters, etc) and you can convert just about anything.

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