My Math Forum What is considered a useless or meaningless fraction?

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 October 26th, 2012, 06:37 PM #1 Newbie   Joined: Oct 2012 Posts: 6 Thanks: 0 What is considered a useless or meaningless fraction? I have been given the task of making an online fraction calculator using VBscript. I would like to add in an element of functionality to reduce the size of fractions in order to make them more meaningful. I was wondering if any experienced people who deal with mathematical equations could comment on what type of fraction would be considered pointless or unusable. I will probably add in a function to show the number as a decimal as well but my main interest is seeing what is considered a pointless fraction. OK, lets put it another way... say for example you had a fraction that was 31742673471/41187659887. As you can see it is pretty useless and is never going to be used because it is actually around about 0.75 or rather 3/4. If you wanted it to remain accurate then you would keep it in decimal form. The essential question I am asking is: What is a usable fraction? At what point do you think a fraction is unwieldy and pointless? I could round the numerator and denominator of that fraction down so that it is 317/419 or I could quite simply say that it is 3/4. I am aware that a fraction like 2/784573 has merit and is usable because it is telling me that there is 2 of a quantity for every 785.6 thousand of another quantity. 16783/784573, on the other hand, is not so useful. Where should we draw the line?
 October 26th, 2012, 07:41 PM #2 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: What is considered a useless or meaningless fraction? IMHO draw the line between the 2 numbers and keep all digits... like this, $\frac{31742673471}{41187659887}$ Seriously, though consider the following... Suppose you make a 1000km train journey with an error of only 10 meters, thats a very small error compared to the whole trip but the train probably goes through a wall at the end of the line. This is just my opinion but i'm biased because i looooove numbers!
October 26th, 2012, 07:51 PM   #3
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Re: What is considered a useless or meaningless fraction?

Quote:
 Originally Posted by agentredlum IMHO draw the line between the 2 numbers and keep all digits... like this...

I think I would let the user decide where to draw the line...some folks want as much precision as possible, while others just want a few digits of precision.
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 October 26th, 2012, 08:10 PM #4 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: What is considered a useless or meaningless fraction? Hey, I learned from the best... http://www.youtube.com/watch?v=Lo4NCXOX0p8
 October 26th, 2012, 08:21 PM #5 Newbie   Joined: Oct 2012 Posts: 6 Thanks: 0 Re: What is considered a useless or meaningless fraction? Hi guys, I think you are completely missing the point to be perfectly honest. I am talking about the use of fractions AS fractions. If you want an accurate number then you use decimals and standard index. I am really looking for people's opinions on the use of fractions as a means to represent a value in a form that is not a decimal. The train journey example is irrelevant because you would not use a fraction under that circumstance - it would be of no value. You could maybe say that you need an accuracy within a tolerance of +1/100 metres or something similar but I would use a decimal instead.
 October 26th, 2012, 08:27 PM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: What is considered a useless or meaningless fraction? To me, a decimal expansion is only accurate if it terminates or repeats (and thus can be expressed as a ratio). I would want the exact fraction, no matter how large the numerator and denominator. But that's just me; some prefer not to work with such cumbersome fractions. That's why I suggest letting the user of your application decide.
 October 26th, 2012, 09:16 PM #7 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: What is considered a useless or meaningless fraction? I didn't mean to offend. When you are erasing numbers from 'vulgar' fractions you have to know what you're doing... $\frac{341191}{489919}$ is nowhere near .75 as a quick glance may imply. I suppose it all depends on desired accuracy.
October 27th, 2012, 06:20 AM   #8
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Re: What is considered a useless or meaningless fraction?

Quote:
 Originally Posted by agentredlum I didn't mean to offend. When you are erasing numbers from 'vulgar' fractions you have to know what you're doing... $\frac{341191}{489919}$ is nowhere near .75 as a quick glance may imply. I suppose it all depends on desired accuracy.
No, your original post did not offend... it was just irrelevant.

No, 341191/489919 does not look like .75 either as a quick or a long glance to anyone with any mathematical ability. In fact it looks like 7/10 (which is obviously easy to convert into a decimal) VBscript does not take quick glances; it is a computer programming language.

Yes, I do know what I am doing.

I am looking for opinions as stated in the original post.

Thank you guys for your efforts. Not quite what I was after but never mind.

October 27th, 2012, 02:18 PM   #9
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Re: What is considered a useless or meaningless fraction?

Quote:
Originally Posted by Cat Face Lord
Quote:
 Originally Posted by agentredlum I didn't mean to offend. When you are erasing numbers from 'vulgar' fractions you have to know what you're doing... $\frac{341191}{489919}$ is nowhere near .75 as a quick glance may imply. I suppose it all depends on desired accuracy.
No, your original post did not offend... it was just irrelevant.

No, 341191/489919 does not look like .75 either as a quick or a long glance to anyone with any mathematical ability. In fact it looks like 7/10 (which is obviously easy to convert into a decimal) VBscript does not take quick glances; it is a computer programming language.

Yes, I do know what I am doing.

I am looking for opinions as stated in the original post.

Thank you guys for your efforts. Not quite what I was after but never mind.
Well, i don't like delivering bad news but your original vulgar fraction is not close to .75 it's closer to .77

You made an error when rounding but i didn't say anything.

You gave

$\frac{317}{419}$

as a rounded specimen, in large font, which led you to believe the original is close to .75 because your error gives about .7566

Should be

$\frac{317}{412}$

The best way to be sure is to perform the entire division without errors.

 October 27th, 2012, 03:50 PM #10 Newbie   Joined: Oct 2012 Posts: 6 Thanks: 0 Re: What is considered a useless or meaningless fraction? Clearly I have made the mistake of feeding you as well. Good bye mymathsforum.

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