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Irrational Numbers
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. While their existence was once kept secret from the public for philosophical reasons, they are now well accepted, yet still surprisingly hard to prove on an individual basis. Please post all questions about irrational numbers, including the famous examples of π, e, and √2, into this category.
3,962 Questions
Which whole number is the irrational root closer to 75?
Square root of 75 is about 8.660254038 so it is 9
How do you do rational and irrational?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
What is the easiest way to figure out the square root of a whole number?
By finding two same numbers that when multiplied together equals the given whole number
Is 1.513513513 irrational number?
No, because it is a rational number that can also be expressed as a fraction in the form of 93/37 if that is recurring 513
This question has depths not yet plumbed by mathematics, science or religion. In trying to answer it I will point to some of those dark holes, saying there lie answers yet to be brought to the light. The first hole is this: when an answer is brought to the light, is the person who went into the dark and emerged again into the light with a new answer a discoverer or an inventor? Much hangs on this.I will make some assumptions about this question. These are* it refers to the Ancient Greeks based in Athens(Athenians)* the 'why was that' part of the question refers to the worry, and not to the never-ending-ness* 'calculated exactly' means expressible finitely in terms of rational numbers* it will be OK to simplify the story a bit (if greater accuracy is required, please ask).The Athenians had built up an arithmetic from the counting numbers (1, 2, 3, . . . .) and made (discovered or invented?) a whole world view based on these numbers. Everything in this world was supposed to be describable in terms of these numbers. Music was, even the music of the spheres was.Ratios between the numbers were permitted, so they were called 'rational' numbers. There is no doubt that among the Athenians there were those with open minds who sought answers even from dark holes, and there were those who 'knew' what they knew, feared dark places, and had closed minds. The latter far out-numbered the former. Remember the fate of Socrates. Remember that in those days there was not the distinction between theology and science that is assumed today.So the majority of the people were certainly dismayed when Eudoxus, not one of their number but an upstart from Asia Minor, came up with the conclusion that the length of the diagonal of a square, the side of which had a rational length, could not itself be a rational number. 'Worry' is not too strong a term for how they felt. Even 'devastation' would be appropriate. How would you feel if everything you thought you knew suddenly seemed wrong? That is how I imagine they felt.The eventual recognition of 'irrational' numbers as real numbers permitted great advances in mathematics. The 'new' became ordinary, but there always was (and perhaps will always be) more 'new' numbers emerging from the dark which will be seen as 'worrying', only to become ordinary in their turn. Witness transcendendals and imaginary numbers (now both universally accepted) and transfinites (almost universally accepted).I may be one of the few still holding out against transfinites. I think that what Cantor drew out of the dark hole should be buried again. I believe Cantor was wrong. This raises a whole new question. Is the 'new' necessarily 'right'? Plus ca change, plus c'est la meme chose.
Are there any irrational numbers?
Yes. In fact, almost all real numbers are irrational numbers.
An irrational number is any number that cannot be expressed as a ratio of two non-zero integers. Examples of irrational numbers are pi (3.14159.....) and e (2.718.....).
What are the number that is irrational?
They are real numbers that cannot be expressed as a ratio of two integers.
Is there inifinitely many irrational numbers?
Yes. In fact, the cardinality of irrational numbers is greater than that of rational numbers.
-6 is rational, as it can be written as 1/b (-6/1).
An example of an irrational number is pi, as it has an infinite amount of decimal places.
How do you define irrational numbers?
Quite simply, a number that is not a rational number. And a rational number is one that can be written as a fraction, with integer numerator and denominator.
Why is pi an irrational number It is Circumference divided by diameter so it should be rational?
It is irrational because its decimal places go on forever. They don't a) end b) have a pattern or c) are the same number repeated
What I was asking was pi is C/d. Circumference is a number and so is diameter. p/q=rational. Then why is pi irrational?
Does the square root of 2 recur?
No.
Only rational numbers have a recurring decimal; √2 is irrational.
Since 1.875 is rational and not irrational, the question makes no sense.
Is 0.06006000600006 rational or irrational?
yes because there is a repeatind decimal like, - 2.24224222422224222224
so that makes -0.0600600060000 rational
