Is a whole number still an integer even if it is written in decimal or fraction form?
e.g.. Is 1.0 an integer? Is 3/1 an integer?

An integer is simply any of the positive or negative whole numbers. It also includes counting numbers, and cannot be a decimal or fraction. If you write in decimal or fraction form it is not considered an integer, but rather a rational number, if it is written with a repeating decimal then you get an irrational number, all being equal in value. Double check with your teacher as I have been to several schools and some text books show this differently.

Here is how I was taught:

http://i56.tinypic.com/nzod4y.jpg

The answer is in my previous post.

The answer is yes - 3/1 is an integer, because 3/1 = 3 which is clearly an integer.

InfoJunkie4Life - I'm afraid that your definitons for rational and irrational numbers are not quite right. Yes, a rational number is one that can be expressed as a fraction or ratio of integers - that part's fine. But the sentence that says "basically a number that can be written as an exact expression" is not. For instance: is an exact expression, but here x is irrational. The better definition is that a rational number is any number that can be written as a fraction, which means that in decimal it is either a terminating decimal (such 1/8 = 0.125) or is a repeating decimal (such as 35/99 = 0.353535... ).

Your definition for an irrational number has a typo - it should say "any number that can not be written as a repeating decimal." Which is equaivalent to saying "any number that can not be written as a fraction." Common examples are and . Your figure implies that rational numbers are a subset of the irrational, but that's not right; there is no number that is both rational and irrational.

By the way, there is a subset of irrational numbers known as "transcendental," which are defined as those that can not be expressed with an algebraic expression (they "transcend" algebra). For example is a transcendental number whereas is not transcendental, because is the root of the polynomial .

Hope this helps to clarify things.