Answer:
0.7 repeating is a rational number simply because it can be written as a fraction. Any number that can be converted into a fraction is a rational number, if the number cannot be expressed as a fraction it is considered to be an irrational number. In this case, 0.7 repeating can be converted into 7/9, therefore it is a rational number.
If you need a more detailed explanation:
x = 0.7(repeating) = 0.77777777
0.79(repeating) × 10 = 7.7(repeating)
10x - x = 7.7(repeating) - 0.7(repeating)
10x - x = 7.7(repeating) - 0.7(repeating) = 9x = 7
9x = 7 (divide both sides by 9)
9x = 7 = 7/9
= 7/9
I hope this helps.