Question

How do you write –0.4 as a fraction? line over 4

Answer 1

Step-by-step 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

`\frac{\cancel{99}x}{\cancel{99}}=(44)/(99)`

`x=(44)/(99)`

Reduce the fraction by 11 and put back the negative sign.

`x=-(4)/(9)`