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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
Why are some of the cubes rational and irrational?
The cubes of all rational numbers will be rational. But the cubes of irrational numbers can be either.
Is six over seven a rational or irrational number?
yes. rational numbers are numbers that can be expressed as fractions and so since 6/7 is a fraction, it is a rational number.
sqrt 9 = +3 or 3
3 - 7 = -4
-3-7 = -10
the sum is an integer
What is the biggest 0 or 100 in rational and in irrational numbers?
100 is bigger and it is a rational number.
No - because it can be represented as a ratio :
5.2 = 520/100 = 52/10 = 26/5 etc.
Any number that can be represented as a ratio of 2 integers is classified as a rational number (other than that you can't use 0 for the denominator)
Why you need irrational number?
To express certain numbers that can't be expressed as a rational number - i.e., that you can't write as a fraction, with integers in the numerator and the denominator.
Can a rational number be an irrational?
Rational numbers and irrational numbers are two completely different groups. A rational number is a number that can be expressed as a fraction of whole integers. An irrational number is a number that cannot be expressed as a fraction of whole integers. So a number is either rational or irrational.
Can a number be both positive and irrational?
Sure - π is positive and irrational.
So is Euler's number "e".
So is √2 (-√2 is of course negative although both roots of 2 square to give 2, the convention is that if there is no sign given, we assume the positive root)
Can an irrational number be a decimal?
If you write an irrational number as a decimal, you would have an infinite number of decimal places, and the digits wouldn't repeat. That is, if you divide 1 by 7 for example, you get the pattern 0.142857 142857 142857... repeating over and over; this won't happen with an irrational number.
All irrational numbers are decimals which can not be expressed as fractions
Is 0.313111331 a rational or irrational number?
It is rational. An irrational number is a number that you cannot define by a fraction or a decimal. Since you wrote it as a decimal, it is rational.
