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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
What is the significance of irrational numbers with explanation?
A rational number is a number which can be expressed as a ratio of two integers. However, there are far more numbers that cannot be expressed in this fashion.
The set of rational numbers is not closed under the basic operation of taking square roots. There are also other operations whose results are not rational numbers. The two most important constant of mathematics are pi (geometry) and e (calculus) and both are irrational numbers.
What is this number - 02089340100?
This number called me and it was a car insurance company (can't remember the name) - however wouldn't accept incoming calls.
What does pi is an irrational number mean?
The number goes on forever and the decimal value is random.
Verify that π is an irrational number?
There is no way to verify something that may or may not be true.
Every natural numaber is a rational number?
No, Natural numbers are defined as non-negative integers: N = { 0, 1, 2, 3, 4, ... }. Some exclude 0 (zero) from the set: N * N = \{0} = { 1, 2, 3, 4, ... }.
A rational number is the ratio or quotient of an integer and another non-zero integer: Q = {n/m | n, m ∈ Z, m ≠ 0 }.
E.g.: -100, -20¼, -1.5, 0, 1, 1.5, 1½ 2¾, 1.75
This means 1 is a rational number and a natural number. Basically anything with a fraction, negative, decimal, or imaginary number in it is not a natural number.
What is an example of a real number that is also an irrational?
The square root of any positive, non-square number will be both real and irrational.
it is irrational because it's from the exponential numbers
Are uneven square roots rational or irrational why?
They are rational because the characteristic of evenness and unevenness is relevant only in the context of integers. And all integers are rational.
Can the perimeter of area of a rectangle ever be an irrational number?
Yes, of course. Why ever not ?
You can make your rectangle any size you want.
Irrational numbers are a subset of real numbers which cannot be written in the form of a ratio of two integers. A consequence is that their decimal representation is non-terminating and non-repeating.
How do you change fractions to decimal and how to determine if it is rational or irrational?
To change a fraction to the equivalent decimal:
Divide the top number by the bottom number.
Regarding rational / irrational:
Not to worry. Every fraction that you can write with numbers is rational,
and so the equivalent decimal is too, even if it never ends.
Can the sum of two irrational numbers be rational if give an example if not explain why not?
1 + sqrt(2) is irrational
1 - sqrt(2) is irrational.
Their sum is 2 = 2/1 which is rational.
