#1**+1 **

*Express as a common fraction the reciprocal of $0.\overline{72}$.*

I can give you the answer.

The decimal equals** 8 / 11 **so its reciprocal would be **11 / 8**.

I can't tell you how to calculate it though. I guessed and got lucky.

I guessed 8/9 ... that was too big, so I guessed 8/11 and that was it.

_{.}

Guest Jun 28, 2022

#2**+1 **

Let \(x = 0. \overline{72}\)

This means \(100x = 72.\overline{72}\)

Subtracting the 2 gives \(99x = 72\), meaning \(x = {72 \over 99} ={ 8 \over 11}\).

The reciprocal of this, as Guest found, is \(\color{brown}\boxed{11 \over 8}\)

BuilderBoi Jun 28, 2022