Question

Express 672727272727 as a rational number, in the form qp

Answer 1

There's a decimal missing somewhere, so I'll just add it wherever, and if it's not correct it shouldn't be to difficult to figure out what to do to fix it.


`x=0.6\overline{72}=0.6727272\ldots`

`10x=6.\overline{72}=6.727272\ldots`

`1000x=672.\overline{72}=672.727272\ldots`


`\implies1000x-10x=990x=666\implies x=(666)/(990)=(37)/(55)`