document.write( "Question 287184: Please help me summarize real - rational and real - irrational numbers for my 7th grader. I know Irr. #'s cannot be expressed as fractions, the decimal never ends and does not have a repeating pattern, and is not a perfect square. But what about negative numbers? rational right? unless it's like -23.7 or such?
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\n" ); document.write( "math Mom \n" ); document.write( "

Algebra.Com's Answer #208184 by jim_thompson5910(35256) $\"\"$ $\"About$

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Negative numbers can be irrational. Consider the number $\"-pi=-3.14159265\"$ (and the digits go on forever without any predictable pattern) which is an irrational negative number. Or look at the number $\"-sqrt%282%29=-+1.41421356\"$ (and the numbers go on...) which is also negative and irrational. Negative numbers can also be rational. Eg. your example of $\"-23.7\"$ is a rational negative number and so is $\"-1%2F2\"$ . So it will all depend on if the number terminates or if there is a pattern with the decimal digits.\r
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\n" ); document.write( "\n" ); document.write( "Just remember that rational numbers are those that can be expressed as a fraction of two integers. Because of this, we can use long division to see that the number either terminates or patterns will emerge in the decimal expansion of the number. On the other hand, irrational numbers are numbers that cannot be expressed as a fraction of two integers. \n" ); document.write( "

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