What is the difference between rational numbers and irrational numbers?

Answer 1

An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. A rational number can be.
A rational number is defined to be a number that can be expressed as the ratio of two integers. An irrational number is any real number that is not rational. A rational number is a number that can be expressed as a fraction. An irrational number is one that can not.

Some examples of rational numbers would be 5, 1.234, 5/3, or -3

Some examples of Irrational Numbers would be π, the square root of 2, the golden ratio, or the square root of 3.
A rational number is a number that either has a finite end or a repeating end, such as .35 or 1/9 (which is .1111111 repeating).

An irrational number has an infinite set of numbers after the decimal that never repeat, such a the square root of 2 or pi.
A rational number is one that can be expressed as a ratio of two integers, x and y (y not 0). An irrational number is one that cannot be expressed in such a form.

In terms of decimal numbers, a rational number has a decimal representation that is terminating or [infinitely] recurring. The decimal representation for an irrational is neither terminating nor recurring. (Recurring decimals are also known as repeating decimals.)
A rational number is a number that can be expressed as a fraction. An irrational number is one that can not.

Some examples of rational numbers would be 5, 1.234, 5/3, or -3

Some examples of irrational numbers would be π, the square root of 2, the golden ratio, or the square root of 3.
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. A rational number can be.
A rational number can be represented by a ratio of whole numbers. An irrational number cannot. There are many more irrational numbers than there are rational numbers
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
A rational number can be expressed as a fraction, with integers in the numerator and the denominator. An irrational number can't be expressed in that way. Examples of irrational numbers are most square roots, cubic roots, etc., the number pi, and the number e.
A rational number can always be written as a fraction

with whole numbers on the top and bottom.

An irrational number can't.
A rational number can always be written as a fraction with whole numbers on top and bottom.

An irrational number can't.

Any number that you can completely write down, with digits and a decimal point

or a fraction bar if you need them, is a rational number.
A rational number can be expressed as a fraction whereas an irrational can not be expressed as a fraction.
Just look at the definition of a rational number. A rational number is one that can be expressed as a fraction, with integers (whole numbers) in the numerator and the denominator. Those numbers that can't be expressed that way - for example, the square root of 2 - are said to be irrational.
A rational number is any number that can be written as a ratio or fraction. If the decimal representation is finite orhas a repeating set of decimals, the number is rational.

Irrational numbers cannot be reached by any finite use of the operators +,-, / and *. These numbers include square roots of non-square numbers, e.g.√2

.

Irrational numbers have decimal representations that never end or repeat.

Transcendental numbers are different again - they are irrational, but cannot be expressed even with square roots or other 'integer exponentiation'. They are the numbers in between the numbers between the numbers between the integers. Famous examples include

e or pi (π).

By definition: a rational number can be expressed as a ratio of two integers, the second of which is not zero. An irrational cannot be so expressed.

One consequence is that a rational number can be expressed as a terminating or infinitely recurring decimal whereas an irrational cannot.

This consequence is valid whatever INTEGER base you happen to select: decimal, binary, octal, hexadecimal or any other - although for non-decimal bases, you will have the "binary point" or "octal point" in place of the decimal point and so on.
A rational number can be expressed as a fraction whereas an irrational number can't be expressed as a fraction
Rational numbers can be expressed as a ratio of two integers, x/y, where y is not 0. Conventionally, y is taken to be greater than 0 but that is not an essential element of the definition. An irrational number is one for which such a pair of integers does not exist.
Rational numbers can be expressed as one integer over another integer (a "ratio" of the two integers) whereas irrational numbers cannot.

Also, the decimal representation of

• a rational number will either:
  • terminate (eg 31/250 = 0.124); or
  • go on forever repeating a sequence of digits at the end (eg 41/330 = 0.1242424... [the 24 repeats]);
• whereas an irrational number will not terminate, nor will there be a repeating sequence of digits at the end (eg π = 3.14159265.... [no sequence repeats]).

Rational numbers are numbers that keeps on going non-stop, for example pie. Irrational numbers end. Its as simple as that!

Improved Answer:-

Rational numbers can be expressed as fractions whereas irrational numbers can't be expressed as fractions.
a rational number can be expressed as a fraction in the form a/b (ie as a fraction).

a irrational number cannot be expressed as a fraction (e.g. pi, square root of 2 etc)
Rational numbers can be represented as fractions.

That is to say, if we can write the number as a/b where a and b are any two integers and b is not zero. If we cannot do this, then the number is irrational.

For example, .5 is a rational number because we can write it as 5/10=1/2

The square root of 2 is irrational because there do not exist integers a and b such

that square root of 2 equals a/b.
Rational numbers can be expressed as fractions whereas irrational numbers can't be expressed as fractions.

Answer 2

A rational number can always be written as a fraction with whole numbers on top and bottom.

An irrational number can't.

Any number that you can completely write down, with digits and a decimal point

or a fraction bar if you need them, is a rational number.

Answer 3

A rational number can be expressed as a fraction, with integers in the numerator and the denominator. An irrational number can't be expressed in that way. Examples of irrational numbers are most square roots, cubic roots, etc., the number pi, and the number e.

Answer 4

Just look at the definition of a rational number. A rational number is one that can be expressed as a fraction, with integers (whole numbers) in the numerator and the denominator. Those numbers that can't be expressed that way - for example, the square root of 2 - are said to be irrational.

Answer 5

By definition: a rational number can be expressed as a ratio of two integers, the second of which is not zero. An irrational cannot be so expressed.

One consequence is that a rational number can be expressed as a terminating or infinitely recurring decimal whereas an irrational cannot.

This consequence is valid whatever INTEGER base you happen to select: decimal, binary, octal, hexadecimal or any other - although for non-decimal bases, you will have the "binary point" or "octal point" in place of the decimal point and so on.

Answer 6

Rational numbers are Real numbers that can be expressed as ratios of two integers. Irrational numbers are Real numbers that cannot be so expressed.

Answer 7

A rational number can always be written as a fraction

with whole numbers on the top and bottom.

An irrational number can't.

Answer 8

A rational number can be expressed as a ratio (hence the name) of two integers. An irrational number cannot be expressed in such a way.

Answer 9

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