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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
Is 27.5 rational or irrational?
It is rational. An irrational number is a number that you cannot define by a fraction or a decimal. Since you wrote it as a decimal, it is rational.
Why square roots are irrational?
Not always as for instance the square root of 16 is 4 which is a rational number but the square root of 2 is an irrational number.
Is there a number that's rational and irrational?
No - the sets of rational and irrational numbers have no intersection.
A rational number is any Real number that CAN be represented as a ratio of two integers where the denominator is not zero.
An Irrational number is any Real number the CANNOT be represented as a ration of two integers.
Is 2.143254324531.an irrational number?
2.143254324531 is the ratio of 2,143,254,324,531 and 1,000,000,000,000 ... nice and rational.
How do you produce an irrational number with no zeros in it?
The number sqrt(2) has no zeros in it, only the digit 2!
If you mean that the decimal representation has no 2 in it, you could create an infinite decimal fraction by selecting, at random, a digit from the set {1,2,3,...,9}. Clearly it cannot have a 0 in it and, thanks to the randomness, it will be irrational.
Where are some places you can find irrational numbers?
Almost anywhere in geometry.
If a circle has an rational radius, its circumference and area will be irrational. Conversely, if the area is rational then the radius will be irrational.
The ratio of the diagonal of a square to its side is always sqrt(2) - an irrational. So if the sides are of rational length then the diagonal is irrational.
There are lots of other common objects where the fact that some of the measures are rational forces other measures to be irrational.
And circles and squares are all around you. Your glass / coffee mug is probably circular. Your plates, bowls etc.
The ratio of the length to width of standard paper (A4) is irrational.
How can you tell if a rational number is repeating without dividing?
If the denominator has ANY prime factor other than 2 or 5, then the decimal is repeating.
If by Salamence the Pokemon and if you mean his Pokedex number, then the answer is 373 if you are referring to the National Dex and 189 if you are referring to the Hoenn Dex.
Is 89.1212121 rational or irrational?
All terminating and repeating numbers are rational.
the square root of non perfect squares and pi are irrational.
Is 8 a rational number or an irrational number?
It is a whole number and it can be written as a fraction, so it is rational.
Are irrational numbers rational numbers?
No. Real numbers are divided into two DISJOINT (non-overlapping) sets: rational numbers and irrational numbers. A rational number cannot be irrational, and an irrational number cannot be rational.
Is -14 a rational or irrational?
14 is rational. Rational numbers are numbers that can be written as a fraction. Irrational Numbers cannot be expressed as a fraction.
No because it can be expressed as a fraction in the form of 30/1
Is negative17 rational or irrational?
Integers are rational numbers, whether they are positive or negative.
Can we include irrational numbers in the set of positive numbers?
Yes, any positive number is a number that doesn't have a (-) behind it (-20; -23.67; -45.45454...), and is not zero (0).
Any repeating number (see 3rd negative example) is irrational, no matter what its sign. Irrational numbers also include numbers (decimals, specifically) that don't repeat, but don't stop. Numbers that don't terminate include pi.
Pi, as it is, is proof of a positive irrational number.
