To express 04 repeating (or 0.4444…) as a fraction, we can follow a simple algebraic method.
Let’s denote the repeating decimal as x:
x = 0.4444…
Now, to eliminate the repeating part, we can multiply both sides of the equation by 10:
10x = 4.4444…
At this point, we have two equations:
- x = 0.4444…
- 10x = 4.4444…
If we subtract the first equation from the second, we can simplify it:
10x – x = 4.4444… – 0.4444…
This gives us:
9x = 4
Now, to find x, we divide both sides by 9:
x = 4/9
So, the fraction representation of 0.4444… is 4/9.