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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
Is irrational used in everyday english?
No, I can go a full week without using it. And I teach mathematics!
Is -0.2929292929 rational or irrational?
It is a rational number because it can also be expressed as a fraction.
What numbers are considered irrational?
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator.
Is Pi divided by root 2 an irrational number?
Yes. This follows from the fact that pi is transcendental. That implies that it can't be written as a root.
1+sqrt(2) and 1-sqrt(2) are both irrational but their sum, 2, is rational.
What is the Need of irrational numbers?
The diagonal of a unit square (1x1) is irrational; the circumference of a circle with diameter 1 is irrational. There are many situations when such measures are required. Also, there are far more irrational numbers than there are rational, so you would be restricting yourself considerably if irrationals were excluded.
What is the product of all the composite numbers less than 10?
Not including 10, it's 3456. Including 10, it's 34560
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
Which whole number is the irrational root closer to 75?
Square root of 75 is about 8.660254038 so it is 9
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
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.
Why is the difference of two rational numbers are rational numbers?
Suppose A and B are two rational numbers.
So A = p/q where p and q are integers and q > 0
and B = r/s where r and s are integers and s > 0.
Then A - B = p/q - r/s = ps/qs - qr/qs = (ps - qr)/qs
Now,
p,q,r,s are integers so ps and qr are integers and so x = ps-qr is an integer
and
y = qs is an integer which is > 0
Thus A-B can be written as a ratio of two integers, x/y where y>0. Therefore, A-B is rational.
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.
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?
-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.
