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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
Would the difference between two irrational numbers is always going to be rational?
No. sqrt(3) - sqrt(2) is irrational.
Is the square root of fraction 196225 irrational or rational?
If you mean the square root of 196/225 then it is 14/15 which is a rational number because it can be expressed as a fraction.
What are the characteristics of real numbers?
The real number system is a mathematical field.
To start with, the Real number system is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility.
In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first.
And finally, a Field is a Ring over which division - by non-zero numbers - is defined.
There are several mathematical terms above which have been left undefined to keep the answer to a manageable size. All these algebraic structures are more than a term's worth of studying. You can find out more about them using Wikipedia but be sure to select the hit that has "mathematical" in it!
How do you find 5 rational numbers between 5 and 5?
-- First of all, the space "between 5 and 5" is zero, so there are no numbers
of any kind in there.
Let's assume that you meant to type "5 and 15".
-- A lot of people don't realize that any number you can completely write down
on paper is rational. So just pick any numbers you like in that range, write them
down on paper, and you'll have your list of rational numbers.
Can have two real numbers if the quotient is not real number?
Yes but only if the denominator is 0 (so the quotient is not defined).
Is zero a rational or an irrational number and why?
Zero is a rational number.
It is because, it can be written as 0/1, which is in the form a/b where, a and b (here a = 0 and b = 1) are both integers and b is not equal to 0.
Pi can't be expressed as a fraction (a ratio of two integers), which makes it irrational. Another way to say it. Pi (π) is an irrational number; it's trancendent. The mathematical proof that pi is irrational can be viewed by using the link to the Wikipedia article on exactly this topic. The challenge is that to understand the proof, one needs some familiarity with integral calculus. Short of that, one would probably have to just accept the fact that pi is transcendent and that it has been proved. (Pi was suspected to be irrational from ancient times, but it was actually proved to be in the 1700's.)
How are irrational numbers being used in the world?
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
Is the change in the value of an account when given to the nearest dollar a irrational number?
No, it is rational.
Why is pi irrational and 3.14 is rational?
pi is an irrational number because it cannot be expressed as a ratio of two integers. In fact, it is a transcendental number, but that is not relevant here.
3.14 is a rational approximation to pi. It is not equal to pi.
Is the fraction 1 over 4 rational or irrational?
It is rational because 1/4= .25
An irrational number (like pi) is a decimal that does not end.
A rational number (think fraction) will end. (ex: 1/8 .35 .83 etc)
5.01001000100001... is not a rational number. Rational numbers will always repeat when written in a digital form.
Since it is not rational, it cannot be written as a fraction with integer numerator and denominator.
What is the proper definition of rational and irrational numbers?
If a number can be written as the ratio of two integers (a fraction with whole
numbers on top and bottom) then the number is rational. If it can't then it isn't.
