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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

Can irrational numbers be classified as a rational number?

No because irrational numbers can not be expressed as fractions whereas rational numbers can be expressed as fractions

Is 37 an irrational number?

-37 is the ratio of -37 to 1 . It's completely rational.

Is 63 divided by 5 an irrational number?

No because it can be expressed as a fraction in the form of 63/5

Which triangle used to represent an irrational number on the number line?

Many right angled triangles can be used. The simplest would be one with legs of unit length.

Is 0.286 rational or irrational?

0.286 is a rational number because it can also be expressed as a fraction

Is 0.000000020 irrational?

0.000000020 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

Does the square 'root of 2 repeat?

No. It is an irrational number and so cannot have a repeating decimal representation (or in any other rational base).

Is 68 an irrational number?

No. If you can write the number on paper, it's rational.

68 is the ratio of 68 to 1.

Is negative two fifteenths a rational or irrational number?

- 2/15 is the ratio of -2 and 15, or of 2 and -15 ... nice and rational.

Why is the sum and product of two rational numbers is rational?

A rational number can be stated in the form a/b where and b are integers. Adding or multiplying such numbers always gives another number that can be expressed in this form also. So it is also rational.

Is -81 an irrational number?

No, -81 is not an irrational number because it can be represented in the form

x/y = -81

Is the number log 36 irrational?

It depends on the base, but for either e or 10, it is irrational.