Question 334191
<font face="Garamond" size="+2">


First change *[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5\ \times\ 10^{100}]


so that it is expressed in the same power of 10 that the other number is in.


So, reduce the exponent by 2, and move the decimal point two places right.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 500\ \times\ 10^{98}]


Now that the decimal points line up, you can just subtract the numbers:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 500\ \times\ 10^{98}\ -\ 6\ \times\ 10^{98}\ =\ 494\ \times\ 10^{98}]


But just subtracting two integers gives you the number of integers between them <i>including</i> one of the endpoints.  Since you want to eliminate <i>both</i> endpoints, you need to subtract 1 more unit.  Furthermore, you need to put the decimal point back where it belongs.


Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (4.94\ \times\ 10^{100})\ -\ 1]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
</font>