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| Rational and Irrational Numbers |
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Rational Numbers
A number that can be written exactly as a fraction is called a rational number.
For example,  ,  , 5,33333... , 6, are all rational numbers.
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5 |
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(rational) |
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If a decimal can be written down exactly, or is a recurring decimal, it is rational.
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| Irrational Numbers
A number such as  is irrational because it cannot be written exactly as a fraction or decimal.
 (pi) is irrational because it is a neverending, non-recurring decimal.
All square roots and cube roots that are not exact are irrational.
Example 1: Find an irrational number between 27 and 35.
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(27 + ) is irrational. |
Example 2: If we square an irrational number, we always get a rational number. Investigate:
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()2 = 4 |
If we square a square root we get a rational number. |
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But ()2 is still irrational. |
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So the statement is incorrect. |
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