Answer:
The pattern in decimal expressions is that the decimal numbers are repeated immediately after the decimal point.
The pattern in the equivalent fraction is that 9 is on all fractions
Step-by-step explanation:
All the cases (0.111..., −0.555..., −1.222... and 5.888...) are solving by the following procedure (only one example is shown):
x = 0.111111...
10x = 1.11111...
10x - x = 1.11111... - 0.111111...
9x = 1
x = 1/9
which is equivalent to express the decimal part as the tenth divided by 9. Then:
−0.555...= −5/9,
−1.222...(repeating)= −1 2/9,
5.888...(repeating)= 5 8/9
