Final answer:
To convert a repeating decimal to a fraction, we can use the formula x = a/ (1 - r), where a is the numerator and r is the common ratio. By substituting the values into the formula, we find that 2.2222... can be written as 20/9.
Step-by-step explanation:
To convert a repeating decimal to a fraction, we will use the concept of a geometric series. Let's call the repeating decimal x. We can write x as a fraction by using the formula x = a/ (1 - r), where a is the numerator and r is the common ratio. In this case, x = 2.2222... and if we let a = 2 and r = 0.1 (since 0.1 is the repeating part), we can substitute these values into the formula.
x = 2 / (1 - 0.1) = 2 / 0.9 = 20/9
Therefore, 2.2222... as a fraction is 20/9.