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Positive and negative numbers are rational numbers and terminating decimals are rational numbers. So, what is an irrational number? Ahhh…you know how you had some of those 'weird' fractions that when you divided you just kept getting a non-terminating decimal that was non-repeating? Well, THAT'S an irrational number. So, let's just concentrate, shall we? on the RATIONAL ones (yeah! the ones that kinda make sense?) right now. (and, girls, the RATIONAL numbers are NOT the 'boy' numbers either! There's no 'gender' attached to the numbers, despite what SOME folks might want you to believe) |
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A rational number is a number that can be written and both a and b are integers. |
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This means that there are basically three types of rational numbers. Let's take a look and see what they are. |
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Based on the above definition, then ALL integers are rational numbers. Why? Well, think about it…you can re-write all integers as fractions if you put 1 as the denominator, right? |
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Terminating decimals can be converted to fractions where the numerator a and denominator b are both integers so this means that terminating decimals are rational numbers. |
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Repeating decimals can always be converted to fractions where the numerator a and denominator b are both integers despite the fact that they have a pattern that repeat so this means that repeating decimals are rational numbers. |
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Note: The repeating section is called the repetend. The bar denotes the part that repeats and is called the vinculum. |
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SO, what does this all mean? IF you come across a number that cannot fit any of the three 'rules' then it is probably (drum roll, please) an irrational number! The famous one you will be dealing with this year is pi (and I am NOT talking about apple pie…silly!).
*Note: There are some 'other' numbers and we'll cover some of them but we won't be covering all of them in our middle school curriculum. In case you are interested…stuff such as, are you ready? Real and imaginary (yes!) numbers! Woo-hoo! Nope, and they're not just in YOUR head either! |
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