Convert 0.1727272... to a fraction in its lowest terms.

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