If you have the repeating decimal 0.777777.... what would you let x equal, and what would you multiply x by?
Let x = 0.7777.... and let 10x = 7.7777..., we get x=7/10
Let x = 0.7777.... and let 10x = 7.7777..., we get x=7/9
Let x = 0.7777.... and let 100x = 7.7777..., we get x=7/99
What about 0.7070707070....?
Let x = 0.7070707.... and let 10x = 7.07070707..., we get x=7/9
Let x = 0.7070707.... and let 100x = 7.07070707..., we get x=7/99
Let x = 0.7070707.... and let 100x = 70.7070707..., we get x=70/99
What about 0.770770770770770....?
Let x = 0.770770770.... and let 100x = 77.0770770..., we get x=77/99
Let x = 0.770770770.... and let 1000x = 770.770770..., we get x=770/999
Let x = 0.770770770.... and let 1000x = 770.770770..., we get x=770/99