EXPLANATION
The bar over 4 indicates the digit is repetitive.
That is;
-0.444444...
First ignore the negative sign and solve
Let x = 0.44444...
Multiply both-side of the equation by 100
100x = 0.44444...*100
100x = 44.444...
Subtract the original x from both-side of the equation.
100x - x = 44.444... - x
Substitute the value of x at the right-hand side of the equation.
99x = 44.444... - 0.4444...
99x = 44
Divide both-side of the equation by 99
[tex]\frac{\cancel{99}x}{\cancel{99}}=\frac{44}{99}[/tex]
[tex]x=\frac{44}{99}[/tex]
Reduce the fraction by 11 and put back the negative sign.
[tex]x=-\frac{4}{9}[/tex]
