# What are rational numbers?

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A rational number is one that can be expressed in the form a/b, if a and b are two integers.

When expressed in the decimal form a rational number either has a finite number of decimal digits, for example 2.5 or 2.1625, or after a finite number of decimal digits, the set of decimal digits repeats itself. For example, the number 3.3333... is a rational number as the decimal digit 3 is one that repeats, this can be written as 10/3. Similarly in the rational number formed by 25/7, the decimal notation is 3.571428571..., here the set of digits 571428 repeat in the decimal digits.

Irrational numbers on the other hand cannot be expressed as a/b, where a and b are integers. Examples of irrational numbers are pi, e, sqrt 3, sqrt 7, etc. When an irrational number is written in the decimal notation, the decimal digits do not form sets that are repetitive. For example, pi = 3.141592654... It is not possible to find a group of digits that repeat even if an infinite number of them are taken.

Any number which is written as a ratio is considered a rational number (e.g.:1.5=15/10=3/2). The numerator of the ratio representing the rational number is integer. The denominator of the ratio representing the rational number is integer and it is not zero. All numbers that are not rational (they can't be represented as a fraction) are irrational (e.g.: sqrt2, sqrt3, sqrt5..)

A number that can be written as an ordinary fraction – a ratio, *a*/*b*, of two integers, *a* and *b*, where *b* isn't zero – or as a decimal expansion that either stops (like 4.58) or is periodic (like 1.315315...). Other examples include 1, 1.2, 385.66, and 1/3.

Rational numbers are countable, which means that, although there are infinitely many of them, they can always be put in a definite order, from smallest to largest, and can thus be counted. They also form what's called a **densely ordered set**; in other words, between any two rationals there always sits another one – in fact infinitely many other ones.

a rational number is any number that can be expressed as the quotient or fraction *a*/*b* of twointegers.with the denominator *b* not equal to zero.