0
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 characteristic of irrational numbers?
They cannot be expressed as a fraction a/b, where a and b are integers (with b non-zero).
None, if the coefficients of the quadratic are in their lowest form.
How can the pythagorean spiral be used to show the exact value of an irrational number?
It cannot. It can only show square roots which represent only a small proportion of irrational numbers.
Is the square root of x and the square root of NEGATIVE x both rational and irrational?
Yes, because when x equals 1, the square root of x is rational and the square root of -x is irrational, and when x equals -1, the square root of x is irrational and the square root of -x is rational.
What rational number has -0.875 as its decimal equivalent?
-8.875 is the same as -0.8750 which is -7/8 as a fraction
Rational thought is employing the logic known as 'thinking' or 'understanding'
Rational Logic doesn't own the 'knowledge' (experience) about reality. For example, intuition makes a deer identify a human as predator because most humans behave like predators.
'Rational thought' or 'understanding/thinking' is applying of the logic 'rationality', designed in Enlightenment by the Catholic pries Descartes. Since application of 'rational' logic is not limited to facts and also include juggling with abstract notions, 'rationality' can also be without emotion and totally abstract (the law is reason without emotion)
Why is the square root of 1000 an irrational number?
The square root of any non-perfect square is an irrational number. Since sqrt(1000) = 10 sqrt(10), it is irrational.
What is the product of rational and irrational number?
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
Is -3.14 an irrational number?
-3.14=(-314/100), so -3.14 is a rational number (since it can be expressed as p/q, with p and q being integers).
If you mean -pi (which is approximately -3.14), then it is irrational. pi is irrational (for a proof, which is fairly complicated, see: http://www.lrz-muenchen.de/~hr/numb/pi-irr.html).
And an irrational number times a rational number (which -1 is since it can be expressed as -1/1) is irrational. This can be proved by assuming the product is rational. Let x be a rational number, which can be expressed as m/n with m and n integers), and let y be the irrational number. Let S=xy. Assume S is rational, and can be expressed as t/u, with t and u being integers. Then:
S=xy
t/u=(m/n)y [Divide both sides by m/n, which is the same as multiplying by its reciprocal, n/m)
(t*n)/(u*m)=y
Since t, n, u, and m are integers, tn and um are integers. (t*n)/(u*m)=y implies y is rational, which is a contradiction. Therefore, xy=S is irrational.
If Dividing a irrational number by an irrational will be a irrational?
Yes normally but if both irrational number are the same then the quotient will be 1
Norinco Reproduction Winchester 97 shotgun Are there any breakdown drawings or schematics available?
The Norinco reproduction of the Winchester 97 pump shotgun was designed by reverse engineering (aka copying) an original Winchester 97. Therefore drawings, schematics and instructions for the original should work for the reproduction. These are routinely available on eBay. At the time of this answer, 360004560026 was one such item.
Is negative 24 an irrational number?
Negative 24 is the ratio of -24 to 1, and also the ratio of 24 to -1, and also the
ratio of -48 to 2, and also the ratio of 48 to -2, and also the ratio of -792 to 33.
Any one of these would be enough to demonstrate that it's a rational number.
Is the square root of 32 an integer or whole number?
The square root of 32 is 5.65685424949238 (or 5.66 rounded).
An Integer is defined as numbers that can be written without a fractional or decimal component.
A Whole Number is not a mathematical term and can either mean Natural Numbers (0, 1, 2, 3, 4....) or Integers (.... -4, -3, -2, -1, 0, 1, 2, 3, 4....).
ie 12345, 980, 5, and -17 ARE integers
.1213, 3.5, 7.999999 and 3.141592 are NOT integers
Numbers that are qualified by root symbols (ie √2 ) or fractions (ie 5½) are NOT integers they are formulae . However, √ and other similar roots of numbers can become integers if when calculated, they result in integers; in this case √9 = 3.
Note:
Integers are numbers and cannot be a formula, therefore √9 being a formula cannot be an integer so if it was required to be stored in a database on a computer as √9 to preserve it's origin (for example) , then it would have to be kept as text where as the product of the calculation (ie 3) could be kept as such because it is an integer.
The fact that a number is negative or positive does not affect it being or not being an integer. The rules above govern whether it is or is not.
Integers are also a data type (2 bytes) used in computing to store numbers ranging in value from -32,768 to 32,767. (whole numbers only).
Are there more rational than irrational numbers?
The answer requires a bit of mathematics, but goes like this:
The product of any 2 rational numbers is a rational number.
The product of any 2 irrational number is an irrational number.
The product of a rational and an irrational number is an irrational number!
Therefore simple logic tells us that there are more irrational numbers than rational numbers. There is a way to structure this mathematically, and I believe it is called an "Inductive Proof".
Interesting !
I'm going to say "No".
I reason thusly:
-- For every rational number 'N', you can multiply or divide it by 'e', add it to 'e',
or subtract it from 'e', and the result is irrational.
-- You can multiply or divide it by (pi), add it to (pi), or subtract it from (pi),
and the result is irrational.
-- You can take its square root, and more times than not, its square root is irrational.
There may be others that didn't occur to me just now. But even if there aren't,
here are a bunch of irrational numbers that you can make from every rational one.
This leads me to believe that there are more irrational numbers than rational ones.
-------------------------------------------------------------------------------------------------------
There are infinitely many more irrationals than rationals; this was proved by G. Cantor (born 1845, died 1918). His proof is basically:
The rational numbers can be listed by assigning to each of the counting numbers (1, 2, 3,...) one of the rational numbers in such a way that every rational number is assigned to at least one counting number;
If it is assumed that every irrational number can be assigned to at least one counting numbers (like the rationals), then with such a list it is possible to find an irrational number that is not on the list; so is it not possible as there are more irrationals than there are counting numbers, which has shown to be the same size as the rational numbers, thus showing that there are more irrationals than rationals.
Is negative two an irrational number?
Rational numbers are those that can be expressed as a ratio of two integers. So 2, which can be expressed in such a way, for example, (-2) / 1 or 2 / (-1) is a rational number.
Are terminating and repeating decimals irrational numbers?
Terminating and repeating decimals are rational numbers.
What is an example of a benchmark number?
It is the number set that everyone shoots for. As an example, in a P.E. class, the benchmark for 8th grade boys in the mile is 8 minutes. Then 8 minutes or less is the time all the 8th grade boys shoot for.
Who invented irrational number?
Sir sinders green, a handsome man in his late 30's first took over a station in kenton soon after did he become a mathematician. he only lived for numbers until his very pretty soon to be wife came along. After a year of marriage, Mrs rebecca swan fell pregnant. This was there 3rd child as the first 2 has died in miscarriage's the aged of 24 Sir. sinders green became a Father drooped maths and became a engineer to earn more money.After 10 years he had 8 children and has suffered a heart attack. Although nurses did the best they could he later died on 28 may
