The Kaufman Decimals

In his brilliant post (read it!), Ben Orlin introduced Kaufman decimals as follows, if

0.(4) = 0.444444444444444444444444444444444444444....,

is a number where the fourths go on forever, then

0.(4)1 = 0.44444444444444444444444444444444444444....1,

is a number where the fourths go on forever and, afterwards, there’s a one.

Imagine writing the number 0.(4)1 into a grid. You fill the first line with fourths and then write "1" into the second line like this