Convert .454545454545........ to a rational number in simplest form.

Answer 1

Let x = 0.454545454545...

Multiplying both sides of the equation by 100, we get:

100x = 45.454545454545...

Subtracting x from 100x, we have:

100x - x = 45.454545454545... - 0.454545454545...

Simplifying, we find:

99x = 45

Dividing both sides by 99, we get:

x = 45/99

To simplify this fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:

x = (45/9) / (99/9)

Simplifying further, we have:

x = 5/11

Therefore, 0.454545454545... is equal to 5/11 in simplest form.