Question

What is 4.54 repeating as a fraction?

Answer 1

`n=0.\dot { 5 } \dot { 4 } \\ \\ \therefore \quad 100n=54.\dot { 5 } \dot { 4 } \\ \\ 100n-n\\ \\ =54.\dot { 5 } \dot { 4 } -0.\dot { 5 } \dot { 4 }`


`\\ \\ =54\\ \\ =99n\\ \\ \therefore \quad 99n=54\\ \\ \therefore \quad n=\frac { 54 }{ 99 } =\frac { 18 }{ 33 }`

Now:


`4.\dot { 5 } \dot { 4 } \\ \\ =4+\frac { 18 }{ 33 } \\ \\ =\frac { 132 }{ 33 } +\frac { 18 }{ 33 }`


`\\ \\ =\frac { 150 }{ 33 } \\ \\ =\frac { 50 }{ 11 } \\ \\ \therefore \quad 4.\dot { 5 } \dot { 4 } =\frac { 50 }{ 11 }`