Question

Jill says that 12.6 repeating is less than 12.63. Explain her error.

Answer 1

12.6 repeating is the equivalent of 12.666666666666 and so on but if you rounded, it would be 12.67. So, compare 12.67 and 12.63. 12.67 is larger.

Answer 2

She is wrong because 12.66 is greater than 12.63. The last digit of 12.66 (6) is larger than the last digit of 12.63 (3) Even if 12.6 keeps on going (12.66666.....) 6 will always be bigger than 3. 
Hope that helped :)