No, it is a rational number. Numbers in the form of a/b, where a and b are integers, are called rational numbers.
0.666... can be written as 20/3. So it is a rational number.
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7 is a counting number. But I am not sure what a counting number number is!
That's the "square" of the number. With counting numbers, the square will always be another counting number.
Yes, and including zero.
If counting by twelves, the tenth number will be 120.
6.7010000000000005