How do people end with .9r? Apart from trying to derive square root of numbers using Newton's method, the biggest culprit is how we employ the authorised order of operation in mathematics i.e. BODMAS, PENDMAS e.t.c. Specificaly where we place the quantities. I saw an equation being used to 'reduce' .9r into 1 (or is it to collapse it into 1?) that went thus x=.9r 10x=9.9r subtracting the first equation from the second and we get 9x=9 dividing each side by 9 we find x=1 proving .9r is actually (equal to) 1. Here is the problem. If we decide to start with division before multiplication, we end up in the same hole that we're trying to get ourselves out of. Check this. (1/9)x9=? Now lets divide 1 by 9, what do we end up with? .111 . . . .i.e. 0.1r multiply that by 9 and we end up with .9r If we could only have re-arranged the equation to be 1x(9/9) That way we will avoid unnecessary controversies (but again just like in tabloids, maths seems to thrive in controversies).