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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.
Who is known for his definition of irrational numbers?
Hippasus, a Pythagorean philosopher is believed to have proven the existence of numbers that are not rational. However, this is not quite the same as "known for". Many (most?) mathematicians would not know who Hippasus was or what he did.
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.
