To convert a repeating decimal to a fraction, we can use the method of multiplying by a power of 10 to eliminate the repeating part.
Let's call the repeating decimal as x.
10x = 4.55555....
Now, let's subtract the original repeating decimal from this:
10x - x = 4.55555.... - 0.45555....
9x = 4.1
To get rid of the decimal, we can multiply both sides of the equation by 10:
9x * 10 = 4.1 * 10
90x = 41
Now, we can divide both sides of the equation by 90:
90x / 90 = 41 / 90
x = 41/90
Therefore, the fraction equivalent of 0.45¯¯¯¯¯ is 41/90.