Convert 0.8181818181 ... to a rational number. Let x be the rational number you're looking for.

Question

x= 0.8181818181 ...
Since there are two digits in the repeating cycle, multiply both sides of the equation by 10^2=100. 100x=81.81818181 ...

Answer 1

To eliminate the repeating decimal, we can subtract x from 100x:

100x - x = 81.81818181 ... - 0.81818181 ...

Simplifying both sides:

99x = 81

Now we can solve for x by dividing both sides by 99:

x = 81/99

We can simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 9:

x = (81/9) / (99/9)

x = 9/11

Therefore, the rational number equivalent of 0.8181818181 ... is 9/11.