# irrational number

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Related to irrational number: imaginary number

## irrational number

any real number that cannot be expressed as the ratio of two integers, such as π

## Irrational Number

a number that is not rational (that is, not an integer or fraction). Real irrational numbers can be represented by an infinite non repeating decimal; for example, √2 = 1.41 …, π = 3.14 …. The existence of irrational ratios (for example, the irrationality of the ratio of the diagonal of a square to its side) was known in antiquity. The irrationality of the number π was established by the German mathematician J. Lambert (1766). However, a rigorous theory of irrational numbers was constructed only in the second half of the 19th century. Irrational numbers are divided into nonrational algebraic numbers and transcendental numbers.

## irrational number

[i′rash·ən·əl ′nəm·bər]
(mathematics)
A number which is not the quotient of two integers.

## irrational number

(mathematics)
A real number which is not a rational number, i.e. it is not the ratio of two integers.

The decimal expansion of an irrational is infinite but does not end in an infinite repeating sequence of digits.

Examples of irrational numbers are pi, e and the square root of two.
References in periodicals archive ?
In present work we don't state the task to find explicit form of irrational numbers fractal.
It is usually simply stated the real numbers are comprised of rational and irrational numbers.
Irrational number is a technical term with a neutral connotation, known by all.
An irrational number has a unique representation as an infinite continued fraction.
Physical objects are postulated entities which round out and simplify our account of experience, just as the introduction of irrational numbers simplifies our laws of arithmetic.
The understanding that this is an irrational number was less secure, and would generally need some more explicit teaching in relation to sets of numbers and their properties).
An interesting irrational number from the exponential series, e is the base of all natural logarithms," the Indian expatriate from Abu Dhabi said.
Pi is an irrational number (a number which cannot be written as a finite or recurring sequence) but mathematically there are an infinite number of these, just as there are an infinite number of rational numbers.
Your students may not have met the irrational number [square root of (2)] in their mathematics courses at this stage, but here is a good place to start.
For the irrational number e, no such measure is usually given.
A few examples of the diverse topics covered in the volumes include acorn worm, air masses and fronts, animal cancer tests, big bang theory, biophysics, buckwheat, cardiac cycle, dentrification, dragonflies, geotropism, ice age refuges, irrational number, legumes, nuclear winter, oscillations, photocopying, quantum electrodynamics, restoration ecology, set theory, squirrel fish, tartaric acid, tumbleweed, ultraviolet astronomy, weather forecasting, xylotomy, and zodiacal light.
The teacher may allow students to explore how the graph of the polar equation above changes if b is an irrational number and why that is the case.

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