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    Trekdawg's Avatar
    Trekdawg Posts: 1, Reputation: 1
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    #1

    Sep 19, 2010, 03:17 PM
    What is an integer?
    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?
    InfoJunkie4Life's Avatar
    InfoJunkie4Life Posts: 1,409, Reputation: 81
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    #2

    Sep 20, 2010, 07:46 AM
    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:
    InfoJunkie4Life's Avatar
    InfoJunkie4Life Posts: 1,409, Reputation: 81
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    #3

    Sep 20, 2010, 12:30 PM
    The answer is in my previous post.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #4

    Sep 21, 2010, 09:50 AM

    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.
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