Show that the recurring decimal 0.13636... can be written as the fraction 3/22

First of all, identify how many digits are recurring in the decimal, in this case it's two: 0.13636...Let x = 0.1363636...Since there are two digits recurring we use 100x = 13.63636... (if it is 1 digit we use 10x, if 3 digits use 1000x and so on)To get rid of recurring decimals, we have to subtract 100x by x because since both numbers have an infinite number of recurring 63, they will cancel each other out.So we get 99x = 13.5, which can also be written as 99x = (135/10)Then we divide both sides by 99 to get x = (135/990)Finally, we simplify the fraction by dividing both the numerator and the denominator by 45, to get x = (3/22)Therefore 0.1363636... = (3/22)