First we must identify the recurring part of the decimal. We see that 72 is repeated, hence it is the recurring part of the decimal. Next, we say x = 0.1727272..., the reason why will become apparent shortly. Now we multiply x by subsequent powers of 10, starting from 100.x = 0.1727272...10x = 1.727272...100x = 17.27272...1000x = 172.7272...We are looking for two multiples of x that have the recurring part of the decimal starting directly after the decimal point, in this case 10x = 1.727272..., 1000x = 172.7272...1000x - 10x = 172.7272... - 1.727272...990x = 171x = 171/990x = 19/110