-1, 0, 1
0 is very definitely an integer.
You can say: two hundred and thirty four thousandths.
Zero is a rational number. It can be written as a ratio: 0/1, 0/2, etc.
From MathsIsFun, here is a formal definition (I copied and pasted, OK)
A rational number is a number that can be in the form p/q where p and q are integers and q is not equal to zero.
Besides, for the set of rational numbers to be closed for addition and subtraction, it is necessary for zero to be a rational number. Example: If you say that you can add any two rational numbers and get another rational number, then what happens if you add 1/2 and -1/2, you get zero, so zero would need to also be a rational number. Yes because it can be expressed as a quotient of two integers. (i.e. 0/1 or 0/2 etc.)
-2.34 is a negative rational decimal.