Question

Find the values of a and b to express this recurring decimal as a fraction.

Simplify this fraction as much as possible before entering your answer.
0.727272... =
`(a)/(b)`
a=
b=

Answer 1

Answer: Let x = 0.727272...

Then, 100x = 72.727272...

Subtracting x from 100x gives:

100x - x = 72.727272... - 0.727272...

99x = 72

x = 72/99

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 9. Therefore:

x = (72/9) / (99/9) = 8/11

So, a = 8 and b = 11. Therefore, the recurring decimal 0.727272... can be expressed as the fraction 8/11.

Explanation: