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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
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.
Which number system is made-up by rational and irrational numbers?
The real number are the union of rational and irrational numbers.
There are none because all integers or whole numbers are rational numbers.
Equations of the form y2 = x3 + ax + b are powerful mathematical tools. The Birch and Swinnerton-Dyer conjecture tells how to determine how many solutions they have in the realm of rational numbers-information that could solve a host of problems, if the conjecture is true.
Why pi is a rational or an irrational number?
Pi is an irrational number because it cannot be expressed as a ratio of two integers.
Can a number be a member of the set of rational numbers in the set of irrational numbers?
No, a number is either rational or irrational
