REAL NUMBERS: A rational or irrational number



Below is a chart that we are going to fill in, but before we do, I want to explain the picture.

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|Largest SET of Numbers in this category (includes ALL other #s from this side ONLY + new): | |

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|Ex: (______________________________) | |

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|Add to the previous | |

|SET to get a newly | |

|NAMED Set (includes | |

|all #s in | |

|second bubble + new): | |

|: |This side includes |

|Ex: (_____________________) |ONE special TYPE |

| |of # ONLY: |

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|Add ONE thing to first | |

|SET to get a newly | |

|NAMED Set (includes | |

|all #s in first bubble + new): | |

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|Ex: (_______________________) | |

| |Ex: (__________________________) |

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|Smallest SET of Numbers | |

|(least amount of | |

|numbers in the set): | |

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|Examples: (__________________) | |

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|NOW, let’s complete the chart with the information you need to know…. |

|REAL NUMBERS: A rational or irrational number. Every point on a number line is a real number |

|RATIONAL NUMBERS: The set of numbers that includes terminating decimals, | |

|Repeating decimals, fractions, and integers. All rational numbers can be written as a fraction. | |

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|Ex: (-3, 1.75, [pic], [pic], 4.25, 0) | |

| |[pic] |

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|INTEGERS: The set of whole numbers and | |

|their opposites. |[pic] |

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|Ex: (…, -3, -2, -1, 0 , 1, 2, 3, …) |IRRATIONAL NUMBERS: |

| |non-terminating (don’t end) |

| |& |

| |non-repeating (no pattern) |

|WHOLE NUMBERS: The set of natural |decimal numbers. |

|numbers AND zero. | |

| |Irrational Numbers cannot be written as a fraction. |

|Ex: (0, 1, 2, 3, 4, …) | |

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| |[pic] |

|COUNTING (NATURAL) NUMBERS: The set of | |

|numbers you learn when you learn to count. |[pic] |

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|Ex: (1, 2, 3, 4, …) | |

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A number can only be RATIONAL or IRRATIONAL, but never BOTH.

RATIONAL #S may be broken down further into other categories, if applicable.

A number, whether RATIONAL or IRRATIONAL, is ALWAYS REAL!

Another way to explain the breakdown of REAL numbers. Consider the following number line illustrations:

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ONE title for ENTIRE chart

THIS side ONLY is broken down into 4 SMALLER categories starting with the SMALLEST bubble working outwards

Chart is broken into TWO different MAJOR categories

When you first learn about #s, you fill in #s on a number line starting with the # 1 and learn to count forever… but, only this side of the # line

RATIONAL #S

INTEGERS

WHOLE #S

COUNTING #S

Then you learn the concept of zero, but you don’t forget about original #s. So, your # line gets longer

REAL #S:

(include all rational & irrational numbers)

A number line is made up of ALL REAL #s (this includes all RATIONAL and IRRATIONAL #s)

FINALLY, to complete your number line, you include IRRATIONAL #s.

RATIONAL Numbers END Here, however, the final # line is below….

Just when you think your #line is complete, you learn about the #s in between, which include terminating decimals, repeating decimals and fractions

-6.65

-1.6

-5.5

7.25

2.5

0.5

6.75

…-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8…

…-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8…

0 1 2 3 4 5 6 7 8…

1 2 3 4 5 6 7 8…

As you get older, you learn the concept of negative #s, but AGAIN, you don’t forget about original #s

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