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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

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?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alex23

Member

Registered: 2012-01-31

Posts: 19

Re: Irrational Denominator

Yes, the latter is more elegant.

Bobbym what do you mean by stable numerically?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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,

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Irrational Denominator

hi bob

or "racionalisati"

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“Here lies the reader who will never open this book. He is forever dead.
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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Irrational Denominator

Thanks everyone.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman