Answer:
[tex]\frac{4}{9}[/tex]
Step-by-step 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 = [tex]\frac{4}{9}[/tex]
Thus 0.444444... = [tex]\frac{4}{9}[/tex]
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 [tex]10^{1}[/tex] as we required 0.4444.. → 4.444...
