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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 4.761 an irrational number?
No. It is a finite decimal number.
An irrational number is one that cannot be expressed as a ratio between two integers, such as pi (which has infinite digits) or square roots of numbers that are not squares of other numbers.
An imaginary number is a different type, such as sqrt (-1), which cannot exist in actuality but appears as a value in higher mathematics.
sqrt 9 = +3 or 3
3 - 7 = -4
-3-7 = -10
the sum is an integer
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.
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)
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.
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 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 126 rational or irrational?
It is a rational number because it can be expressed as a fraction in the form of 63/50
What is the biggest 0 or 100 in rational and in irrational numbers?
100 is bigger and it is a rational number.
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)
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.
