Question

What is 0.24 ̅ (4 is repeating) expressed as a fraction in simplest form?

Answer 1

11/45 

10x=2.44

10x - x = 2.44- 0.24

9x=2.2


2.2/9 =22/90

Answer 2

Here, we need to find express 0.2444... as a fraction in simplest form.

Let the fraction be expressed as x

Now,

x = 0.2444....

Since, x is recurring in 1 decimal places, we multiply it by 10.

10x = 2.4444....

From left hand-side, x is subtracted and from 0.24444... from right hand side

10x - x = 2.4444.... - 0.24444....

So now,

9x = 2.2

x = $\frac{2.2}{9}$

x = $\frac{22}{90}$

x = $\frac{11}{45}$

Thus, fraction as simplest form = $\frac{11}{45}$