Question

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

Show your work please

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 =
`(2.2)/(9)`

x =
`(22)/(90)`

x =
`(11)/(45)`

Thus, fraction as simplest form =
`(11)/(45)`