The question goes like this, given a recurring decimal like the one below, can you determine a fraction that equals it:
Well, the trick is to recognise that you can make use of the commutative properties of algebraic manipulation as follows:
And then by equating the two equations we must concur that:
But of course, for those budding Mathematicians out there, you may have seen this as a simple Geometric Progression sum to infinity, and therefore the general formula follows directly for such a sum:
I'm taking for granted that all of you know what Geometric Progressions are, haha.