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October 26th, 2012, 06:37 PM   #1
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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?
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October 26th, 2012, 07:41 PM   #2
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Re: What is considered a useless or meaningless fraction?

IMHO draw the line between the 2 numbers and keep all digits... like this,





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!

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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...
[attachment=0:nhq28adc]wiseguy.jpg[/attachment:nhq28adc]



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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File Type: jpg wiseguy.jpg (5.5 KB, 719 views)
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October 26th, 2012, 08:10 PM   #4
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Re: What is considered a useless or meaningless fraction?

Hey, I learned from the best...

http://www.youtube.com/watch?v=Lo4NCXOX0p8

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October 26th, 2012, 08:21 PM   #5
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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.
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October 26th, 2012, 08:27 PM   #6
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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.
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October 26th, 2012, 09:16 PM   #7
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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...

is nowhere near .75 as a quick glance may imply.

I suppose it all depends on desired accuracy.

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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...

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.
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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...

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



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



which gives about .7694

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

Lower in your original post, you made another rounding error...

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October 27th, 2012, 03:50 PM   #10
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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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