This is insightful, but hard to read. Essentially: 1/3 * 4 = 4/3 4/3 = 1 + 1/3 So, working backwards, our number can be more and more closely approximate

This is insightful, but hard to read. Essentially: 1/3 * 4 = 4/3 4/3 = 1 + 1/3 So, working backwards, our number can be more and more closely approximated by repeatedly adding 1 and dividing by 4 - or in binary, prepending a 1 and shifting two places right: 0.01010101...