Please help!!!!!!!!!!!!!

How can we prove that 1.9(and the nine is going on forever, and there is a line that is suppose to be on top of the 9) is equal to 2, without using rounding? Explain.

Question

Please help!!!!!!!!!!!!!



How can we prove that 1.9(and the nine is going on forever, and there is a line that is suppose to be on top of the 9) is equal to 2, without using rounding? Explain.

anonymous · Answer

Well,

anonymous · Answer

You can use division as proof...

anonymous · Answer

$$x=1.999...\10x=19.999...\9x=18\x=2$$

anonymous · Answer

I don't really know how to show you though...

anonymous · Answer

I could show you with the logic of limits.

anonymous · Answer

Sure

anonymous · Answer

But before why did you start with 10? How did you get it?

anonymous · Answer

$$1.99999... = \lim_{^{x} \rightarrow \infty} 2-(0.1)^{x}$$

anonymous · Answer

@Rana12333 multiplying by 10 yields as follows...$$10x=1.999...\times10\\ \ \ \ \ \ =19.999...$$Then, you may subtract from both sides.$$10x-x=19.999...-x\9x=19.999...-1.999...\\ \ \ \ =18$$Now, divide to isolate x.$$x=2$$

anonymous · Answer

Here, the expression (0.1)^x will approach 0

anonymous · Answer

Either odrin's or my explanation will work, but I actually like his better.

anonymous · Answer

But why did you chose the number 10?

anonymous · Answer

He chose 10 because that will shift the decimal point conveniently.

anonymous · Answer

I multiplied by 10 in order to do the proof.

anonymous · Answer

Can you explain it step by step so I can understand it better please

anonymous · Answer

http://en.wikipedia.org/wiki/0.999...#Algebraic_proofs

anonymous · Answer

I need 1.999999999999999999........, not 0.99999999999..........

anonymous · Answer

$$1.999... = 1+0.999...$$