Question

Can anyone please help me solve this question? (If you can, of course)

Answer 1

`(4)/(9)`

Explanation:

Create 2 equations with the repeating number after the decimal point, then subtract the equations to eliminate the repeating number.

let x = 0.4444.... → (1) ← multiply both sides by 10

10x = 4.4444.... → (2)

Subtract (1) from (2) eliminating the repeater

9x = 4 ( divide both sides by 9 )

x =
`(4)/(9)`

Thus 0.444444... =
`(4)/(9)`

To know which power of 10 to multiply by

The power of 10 is the value to ensure the repeating 4 is after the decimal point.

Here it was
`10^(1)` as we required 0.4444.. → 4.444...