Rational and Irrational Numbers Defined and Explained

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Rational Numbers Definition

A real number that can be written or expressed as a ratio of two integers is rational.

All integers, positive or negative are rational numbers because they divide by 1.

Zero is a rational number that can be written as a ratio of two integer numbers, as 0/1.

Rational numbers can be written or expressed as either an ordinary (terminating) decimal or as an infinite repeating decimal.

Rational Numbers Examples:

    It can be written as 5.0, an ordinary decimal.

   .090909… The decimal portion 09 repeats.

   The decimal value never terminates.

   equivalent is .6666666… The decimal is infinite

   repeating, but never terminates. It is a rational number.

   It is a decimal that terminates, but does not repeat.

   It is a rational decimal.

   is 2. 2 can be written as 2/1. There is no decimal place

   value for 2 or 2/1. It is a rational square root number.
   Some other rational square root numbers are:

   √9, √16, √36, √49, √64.

Rational Numbers

Irrational Numbers Definition

Real numbers that cannot be written as a ratio of two integers are irrational. They are decimal numbers that both do not terminate and do not repeat. Irrational numbers are infinite non-repeating decimal numbers.

Irrational Numbers Examples:

    is 1.4142135… The decimal never repeats and never     terminates. It cannot be written as a ratio of two integers.

    It is an irrational square root number.

    √3, √5, √7, √10, 2 + √2, 4 − √7.

    It cannot be written as a ratio of two integers. It is an

    infinite non-repeating decimal number.

    It cannot be written as a ratio of two integers. It is an

    infinite non-repeating decimal number.

    of two integers. It is irrational.

Irrational Numbers.Top of Page

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