Question

What is 72.1 repeating as a fraction

Answer 1

Let

$x=72.111...$

Multiply x by a power of  $10$, one that keeps the decimal part of the number the same:  

$10x=721.111..$

Subtract $x$ from $\\10x$

$10x-x=721.111-72.111=649$

The repeating decimals should cancel out

$\\9x=649$

solve for x

Divide by $9$ both sides

$9x/9=649/9$

$x=649/9$

therefore

the answer is

The fraction  is $\frac{649}{9}$

Answer 2

$x=72.\overline{1}\\ 10x=721.\overline{1}\\ 10x-x=721.\overline{1}-72.\overline{1}\\ 9x=649\\ x=\dfrac{649}{9}$