Converting a recurring decimal to a fraction
For a couple of hours a week I am doing a beginner's level maths course. The topic today was converting recurring decimals into fractions. For example (the [] are the repeating digits 0.[6] 1x = 0.[6] 10x = 6.[6] 9x = 10x - 1x 9x = 6.[6] - 0.[6] = 6 Therefore the answer is 6/9, or 2/3 When it got to numbers like 0.12[34] (ie 0.12343434343434.....) the lesson was really complicated, but I came up with a more simple approach, so here it is if ever you need it. My first observation was that we need a large number and a small number. So let's start with the 10x we used above 1x = 0.12[34] 10x = 1.2[34] therefore 9x = 10x - 1x which is 1.2[34] -0.12[34] This is going to give us 1.1(something) My second observation is that fractions cannot have decimal values in them. In order to get rid of the fraction we need the big number to have the exact same fraction as the small number. e.g. B.[34] -S.[34] =X.[00] So our small number needs to end with [34]. Given the number 0.12[34]