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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.
500 Questions
Can a number be a rational number and not an integer?
Asked by Wiki User
Yes, just look at decimals.
Note: integers are a subset of rational numbers.
Show that set R of real numbers is a group with respect to multiplication?
Asked by Wiki User
Closure: If x and y are any two elements of Rthen x*y is an element of R.
Associativity: For and x, y and z in R, x*(y*z) = (x*y)*z and so, without ambiguity, this may be written as x*y*z.
Identity element: There exists an element 1, in R, such that for every element x in R, 1*x = x*1 = x.
Inverse element: For every x in R, there exists an element y in R such that x*y = y*x = 1. y is called the inverse of x and is denoted by x^-1.
The above 4 properties determine a group.
Is .786666666666... rational or irrational?
Asked by Wiki User
Assuming that the notation "666..." represents the number with infinitely many 6s, the number is rational.
What is the number for 911?
Asked by Wiki User
Just dial number 911 on your telephone to reach an emergency operator. The emergency operator will connect you to the police, the fire department, or whatever you need. However, 911 doesn't work everywhere, the numbers can vary depending on where you live. The best way to get in touch with someone in an emergency is just dial "0" for an operator. It is best not to fake a 911 call, because it is an emergency line and if one pulls a prank call, one can receive an expensive ticket.
Is -5 and two thirds an irrational number?
Asked by Wiki User
No. It's the ratio of -17 and 3 ... a perfectly rational number.
Is the square root of -16 irrational?
Asked by Wiki User
No, the square root is 4 so that means it is rational because it can be turned into a fraction!
What indicates that the roots of a quadratic are irrational?
Asked by Wiki User
In the quadratic equation, b^2 - 4ac < 0.
Is every real number either a rational number or a irrational number?
Asked by Wiki User
Yes. A real number is any comprehendable number, from negative infinity to positive infinity. A rational number is any number that can be the answer to a division equation; an integer, fraction, or a decimal. An irrational number is any number that cannot be expressed as a fraction; such as exponents.
Is -81 is rational or irrational?
Asked by Wiki User
81*81 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
