Question 178091: what is irrational numbers and what is rational numbers?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! a rational number is a number that you can make a ratio out of with an integer on top and an integer on the bottom.
1/2 is a rational number.
3/4 is rational.
7/9 is rational.
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an irrational number is a number that you cannot make a ratio out of using integers on the top and integers on the bottom.
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a rational number can be never ending when you take the decimal equivalent.
2/3 would be an example:
2/3 = .6666666666666666666666666666666666666666666666666..........
while the decimal is never ending, it is still a rational number because it is the result of a ratio of two integers.
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if you see a never ending decimal, and you see a recognizable pattern, then the number is most likely a rational number.
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if you see a never ending decimal, but you cannot see a recognizable pattern, then the number is most likely an irrational number.
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from the web:
Definition: A rational number is a number that can be represented as a fraction m/n, where m and n are integers, and n is not equal to 0.
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one website said pi was a rational number.
another said it wasn't.
i agree with the one that said it wasn't because the decimal goes on and on and there is no recognizable pattern to the digits.
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square root of 4 is a rational number because the answer is 2 and any integer is a rational number since it can be expressed as the ratio of 2/1.
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the square root of 3 is not a rational number.
take the square root of 3.
the decimal equivalent of that is:
1.732050807568880000000000000000
this number goes on and on but there is no recognizable pattern to the digits.
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take 1/7.
the decimal equivalent of that is:
0.142857142857143000000000000000
while this number goes on and on, there is a recognizable pattern to the digits.
142857 then 142857 then 143000 which is probably 142857 but the software package i used (microsoft excel) stopped after so many significant digits and then rounded.
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pi is not a rational number.
this is the microsoft excel representation of pi up to 15 significant digits.
3.141592653589790000000000000000
as you can see, there is no recognizable pattern to the digits.
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the strict definition is as stated above (m/n when m and n are integers and n not equal to 0).
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recognizing a decimal equivalent as a rational number is a little more difficult because most calculators and even software programs don't go out far enough to let you see a pattern if there is one. if the pattern shows up early you're home free. if the decimal equivalent is not never ending, i.e. it is a discrete number of digits, then the number for sure a rational number.
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take .643105
this number has a finite number of digits and can be expressed as 643105/1000000
which are both integers.
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