
Re: A question of orders of magnitude
Posted:
Dec 1, 2012 11:19 AM


Olumide wrote: > > On 1 Dec, 01:03, Virgil <vir...@ligriv.com> wrote: > > In article > > <e98ccc3507b74ac38059c0d5b98b2...@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

