0.9 repeating = 1?

[Ian Curtis]

Originally Posted by jmanela

I was googling around today and i came across something rather odd. http://en.wikipedia.org/wiki/0.999.... Now, this wikipidia page claims that .99999 repeating = 1.

Here is a quick algebraic proof to support this,



Now that is an algebraic point of view. I can't speak for calculus because i haven't taken that yet. What is your view on this topic?

You don't need calculus for this, just Series and Sequences which is an Algebra II/Precalc class. (You will make extensive use of series and sequences in Calc II and you will learn to hate them )

http://en.wikipedia.org/wiki/Geometric_series

Consider .9~ to have a seed value of .9 with a ratio of .1. Use the formula proven on the wiki page. Voila!

They also do an example problem under Repeated Decimals.