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Topic: A question of orders of magnitude
Replies: 7   Last Post: Dec 3, 2012 4:21 AM

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Frederick Williams

Posts: 2,164
Registered: 10/4/10
Re: A question of orders of magnitude
Posted: Dec 1, 2012 11:19 AM
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Olumide wrote:
>
> On 1 Dec, 01:03, Virgil <vir...@ligriv.com> wrote:

> > In article
> > <e98ccc35-07b7-4ac3-8059-c0d5b98b2...@g6g2000vbk.googlegroups.com>,
> >
> > Olumide <50...@web.de> wrote:

> > > I'm reading a book in which the author compares two pairs of numbers
> > > (0.31, 0.39) and (6.10,0.39) and multiplies the second member of each
> > > pair by a factor R_1 = 2 and R_2 = 20 so that both members of the pair
> > > "have the same order of magnitude". Subsequently the pairs of numbers
> > > become (0.31, 2 x 0.39) and (6.10 , 20 x 0.39). I'd appreciate help
> > > in understand how these numbers satisfy the stated condition.
> > >

> > Roughly speaking, two numbers are of the same order of magnitude if
> > their quotient is between 1/10 and 10 in absolute value, thus
> > multiplying or dividing a number by 10 causes a change in order of
> > magnitude.

>
> Thanks Virgil. I understand the rough jist of orders of magnitude from
> Wikipedia your reply, but I'm still at sea witb the specifics. Both
> numbers in the pairs to seem to me to have the same order of
> magnitude.
>
> First pair : 0.31/0.39 = 0.79487
> Second pair: 6.10/0.39 = 15.6410


Since 15.6410 > 10, the second pair aren't of the same order of
magnitude. What is the author trying to achieve?

> [Post factoring]
> First pair : 0.31/(2 x 0.39 ) = 0.3974
> Second pair: 6.10/(20 x 0.39 ) = 0.521



--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting



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