Problems with scientific notation!

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GAK

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Hi, I'm a novice student of Salman Khan's online 'math's academy', but right now I'm flummoxed by a monster maths problem. It's got less to do with the hugeness of the numbers involved (though that's bad enough); rather it's my lack of maths knowledge/technique that's the real issue here. So here goes:

6.09e1012 squared divided by 1,256.6 squared.

I'd appreciate it if anyone can explain to me how this can be solved. Many thanks.
 
First, a2b2=(ab)2\displaystyle \frac{a^2}{b^2}= \left(\frac{a}{b}\right)^2 so it may be simpler to divide first, then square:
6.09×1010121256.6=6.091.2566101012103\displaystyle \frac{6.09\times 10^{1012}}{1256.6}= \frac{6.09}{1.2566}\frac{10^{1012}}{10^3}.

Can you do those? It helps to know that 10x10y=10x−y\displaystyle \frac{10^x}{10^y}= 10^{x- y} and that (10x)2=102x\displaystyle (10^x)^2= 10^{2x}.
 
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Yes, I can begin to see the logic of it now. I'm still not sure if I can solve it, but I'll give it try. Many thanks.
 
Well, along with some help from a friend of mine, this is my solution: (6.09e1012) squared, divided by (1256.6) squared equals 280,662,609.37023 divided by 1,579,043.56

= 177.7421639782.

Now this answer seems to be so preposterously wrong that I scarcely know how to confront it. It is all the more evidently so when you consider that 6.09e1012 refers to the surface area of the Sun in square kilometres, while the other represents, again in square kilometres, the surface area of a sphere just twenty kilometres in diameter. As a result, I find it quite impossible to imagine how the latter sum goes into the former a mere 177.7 times! :(
 
GAK said:
Hi, I'm a novice student of Salman Khan's online 'math's academy', but right now I'm flummoxed by a monster maths problem. It's got less to do with the hugeness of the numbers involved (though that's bad enough); rather it's my lack of maths knowledge/technique that's the real issue here. So here goes:

6.09e1012 squared divided by 1,256.6 squared.

I'd appreciate it if anyone can explain to me how this can be solved. Many thanks.
Click to expand...
 [6.091.2566]2∗[101012103]2\displaystyle \ \left[\dfrac{6.09}{1.2566}\right ]^2 * \left[\dfrac{10^{1012}}{10^3}\right ]^2 = 23.4877 * 102018
 
Subhotosh Khan said:
 [6.091.2566]2∗[101012103]2\displaystyle \ \left[\dfrac{6.09}{1.2566}\right ]^2 * \left[\dfrac{10^{1012}}{10^3}\right ]^2 = 23.4877 * 102018
Click to expand...

Except it is e1012 not 101012. Converting e1012, we have e1012 ~ 3.20638513 * 10439
 
Subhotosh Khan said:
As far as I know, in scientific notations, (U.VW E XX) means (U.VW * 10XX )
Click to expand...

That's only if you don't march to the beat of a different drummer. I was sure I saw a ^ between the e and 1012. I think I going blind in one eye and can't see out of the other.
 
As Subhotosh Khan pointed out, it really should have been "E1012" not "e1012". If it had been written correctly you wouldn't have had that confusion.
 
HallsofIvy said:
As Subhotosh Khan pointed out, it really should have been "E1012" not "e1012". If it had been written correctly you wouldn't have had that confusion.
Click to expand...
Oh, I've seen it written with the small e. In fact, back when I was a pup and learning this moderately new language FORTRAN, I seem to remember I used the small e almost all the time (maybe just to be different though). Of course, machines at that time didn't know the difference between upper and lower case (or maybe it was the people we sent the code sheets to for the punched cards always used upper case anyway).
 
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In MS_Excel, if you type

=3e2

(small or uppercase e)

it will return

300
 
Ah, yes, I understand now. I mistook the notation for what it was, and so compounded the problem. My apologies.
 
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