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#1 2012-02-29 14:33:56
- MathsIsFun
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Irrational Denominator
I was recently emailed by a teacher that I had an Irrational Denominator on one of my pages. I amended it so that students would not get into trouble.
Just a throwback from the past? What do you guys think?
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#2 2012-02-29 14:40:34
- bobbym
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Re: Irrational Denominator
Hi;
Both forms are obviously correct although the rationalized denominator is slightly more stable numerically. I would think they should only take points off for the first form if the question states rationalize the denominator.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#3 2012-03-02 06:40:38
- Alex23
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Re: Irrational Denominator
Yes, the latter is more elegant.
Bobbym what do you mean by stable numerically?
#4 2012-03-02 07:10:59
- bobbym
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Re: Irrational Denominator
Hi Alex23;
Slightly larger denominator. Multiplication tends to smear out significant digits and division by large numbers does not. One is an error amplifier(multiplication) and one is an error reducer. This is only a very rough definition but it is how I understand it. Division by a bigger constant is slightly better,
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#5 2012-03-02 09:06:19
- bob bundy
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Re: Irrational Denominator
hi MathsIsFun,
When I was young we had to do all our calculations long hand or by use of log tables. (computers were still steam driven in those days and each one filled a building!)
So it made sense to rationalise denominators. We were also made to learn that
√ 2 ≈ 1.414
√ 3 ≈ 1.732
√ 5 ≈ 2.236
It's surprising how many calculations could be done with just that.
But now we have calculators. Does it matter any longer? I think like bobbym, only if the question says you must rationalise. Or rationalize. ( depending on where you are in the world :-) )
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#6 2012-03-02 09:15:33
- anonimnystefy
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Re: Irrational Denominator
hi bob
or "racionalisati" 
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#7 2012-03-02 12:10:45
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Re: Irrational Denominator
Thanks everyone.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman