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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 number is real and irrational?
Every real number is either rational, or irrational. Examples of irrational numbers include:
* The square root of any positive integer, except that of a perfect square.
* The number pi.
* The number e.
* Any of the above, multiplied by or added to a rational number - for example 2 x pi, 2/3 times the square root of 2, etc.
* An expression like 10 to the power x is irrational for most values of x.
Does percents are rational or irrational?
It depends on the percentage.
A 1 cm arc of a circle whose radius is 1 cm will represent 100*1/(2pi) % = 50/pi % and that is an irrational percentage.
A semicircular arc of the same circle will represent 50%, which is rational.
What is the Next to rational and irrational number?
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).
How whole numbers integers rational numbers and irrational numbers came?
When pre-historical people started counting - their friends (or members in their "gang"), their enemies, the numbers of prey animals or how many days away there was water or good hunting - they counted in integers.
That was fine until they needed to share things. And that is when ratios or rational numbers came in.
However, once they started studying mathematics - geometry in particular - they found that some problems could not be solved using rational numbers. For example, if you had a square with unit sides, its diagonal could not be rational. A circle with unit radius did not have a unit circumference. Irrational numbers were introduced to deal with this shortcoming.
If you are 62 what year were you born?
If you were birthday is between 1 January and today's date (8 January) then you were born in 1948. If your birthday is between 9 January and 31 December then you were born in 1947.
What is the classification of the product of a rational and an irrational number?
If you multiply a rational and an irrational number, the result will be irrational.
What real numbers cannot be graphed on the number line?
Theoretically, no real numbers cannot be graphed on the number line. The number line contains all real values. Practically, it is not really possible to exactly place an irrational number, as it is a non-terminating, non-repeating decimal. But for all intents and purposes, you can place it at least to the tenth or hundredth place, which is about all you can discern with the naked eye, anyway!
Is the product of rational no and irrational no is rational?
Unless you multiply 0 with some irrational number, it is impossible. Here's why:
Let x,y be rational with x = a/b, z = c/d and y be the irrational number. If we presume xy = z then we have y = z/x. However, this is equal to (c/d)/(a/b) = (bc)/(ad), which is rational. Since y is assumed to be irrational, this cannot occur (unless one of b,c is zero).
Is 2.24224222422224222224 a rational or irrational?
Assuming -2.24224222422224222224 repeats, it is irrational. Rational numbers are numbers that can be written as a fraction. Irrational Numbers cannot be expressed as a fraction.
Can two rational numbers makes irrational numbers?
Yes.
2 and 0.5 are both rational. But 2^0.5, which is sqrt(2), is irrational.
What is the symbol of irrational numbers?
There is no special symbol.
The set of rational numbers is denoted by Q and the set of real numbers by R so one option is R - Q.
Is -5 an integer and an rational number?
-5 is an integer and a rational number.
Integers can be positive or negative.
Rational numbers can be expressed as a fraction of integers.
When is a fraction irrational?
If, in its simplified form. its numerator or denominator (or both) are irrational.
What is an example of a cubic number?
Every real number is a cubic number: it is the cube of its cube root!
