Express the following rational number in the form of a fraction

0.18181818.....

Please help me with clear working out as well

x = 0.18181818...
100x = 18.1818181...
99x = 18.1818181... - 0.1818181....= 18
x = 18/99 = 2/11

In order to make this into a fraction you will need to use two equations, followed by linear combination (adding or subtracting the like-terms from each equation to get one equation.)

The decimal is 0.181818181818.... and this will continue on forever...
So we can say:

x = 0.18181818181818....

x being the fractional version of the decimal.

Now we need to write an equivalent equation that will let us cancel the repeating decimal digits. So we can say:

100x = 18.18181818181818....

This is because all we did was multiply both sides by 100.

Now we have:
100x = 18.18181818181818....
x = 0.18181818181818....

Subtract through linear combination and we get:
99x = 18

The .181818... of each equation cancel each other.

Divide both sides by 99 to get x = 18/99
But we can still simplify because both 18 and 99 are divisible by 9. So the final answers is:

x = 2/11

Hope that helps!

Any non terminating decimal must have the denominator of 99 because it is not exactly whole.
Since 18 is repeating, make it 18/99.
Reduced is 2/11

The answer is 18/99, and here is how you get it: .18181818....... =
1/10[ 1 + 1/100 + 1/10,000 + .......... +
8/100[ 1 + 1/100 + 1/10,000 +..........
=10/99 + 8/99 = 18/99