Solving for 100x: A Math Puzzle

[thomas49th]

Hi, I recall a thingy when you have somthing like

x = 0.91919191

then you go 100x = 91.919191
100x - x = 91

When do you use this? It's in conjuction with somthing else... looked in my textbook can't find it.

Thanks

 

[mbrmbrg]

Personally, I use that when I have a repeating, non-terminating decimal that I want to get in fractional form so it looks prettier in an equation.

 

[arildno]

Why should you care "when is it used"?
It is a wrong question; the technique is never "used"; rather, it illustrates how you may rewrite a periodic decimal as a fraction.

That is, the technique amounts to a constructive PROOF of a certain mathematical proposition:
namely that any periodic decimal can be written as a fraction between two natural numbers, i.e a periodic decimal is necessarily a rational number.

 

[Gib Z]

100x - x=99x=91

x=91/99

Thats why its used, to get urself a fraction.