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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 3over4 rational or irrational?
irrational, if it's is not tons of #s after the decimal that means its terrminating irrational
Why is 3.14 rational but π is not?
3.14 has a finite number of digits. All numbers with a finite number of digits are rational. Pi has an infinite number of digits, AND the digits don't repeat in a regular pattern. (Numbers with repeating decimals are rational as well.)
Numbers that can be expressed as fractions are rational
Well, for example, the square root of 4 is 2, which is a rational number. As long as the number which is being square rooted is not a square number itself (i.e. 1, 4, 9, 16 etc.), then it will be irrational.
So.....
the square roots of 49, 100, 196, for example, are all rational numbers (7, 10 and 14 respectively.)
They do not have to be integers. The square of of any rational number automatically has a rational square root eg the square root of 77.41792 is 77.4179 . Rational means expressable as a ratio of integers: 77.4179 is 774179/10000 .
Can an irrational number be a decimal if so give an example?
Irrational numbers are decimal numbers that can't be expressed as fractions. An example is the square root of 2
Is 3 over 4 an irrational number?
No, an irrational number by definition is a number that cannot be written as a fraction
Can negative decimals be a rational number?
Yes, as long as the decimal does not go on forever without repeating.
My number is 11.
Who discovered pi is irrational no?
It was known from ancient times that pi is irrational. However, that fact was proven in 1761 by the Swiss scientist Johann Heinrich Lambert.
Are irrational addition numbers closed under the closure property?
No. For example, the square root of two plus (minus the square root of two) = 0, which is not an irrational number.
Why the set of irrational number is denoted by q'?
The set of irrational numbers is NOT denoted by Q.
Q denotes the set of rational numbers. The set of irrational numbers is not denoted by any particular letter but by R - Q where R is the set of real numbers.
Why is 37 square root an irrational number?
The same reasoning you may have seen in high school to prove that the square root of 2 is not rational can be applied to the square root of any natural number that is not a perfect square.
Why rational numbers require extension?
Because numbers such as pi, e and the square root of 2 are not rational.
Can you divide a rational number by an irrational number and the answer is rational?
Yes, but only if the starting rational number is 0.
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was used by Kurt Gödel for the proof of his incompleteness theorems.
