What is a rational or irrational number?

Answer 1

A rational number has a pattern or an end like 406, 3.645645645, or 5.77777777......etc.

An irrational number has no pattern and goes on forever (never a whole number) like pi: 3.14159.......

Answer 2

A rational number is a real number that can be written in the form of a/b, where a and b are both integers.

An irrational number is a real number that is not rational.

For example, 2/3 and -15/4 are rational. "0.25" is rational because it can be written as 1/4. "0.333333..." (with the 3s going on to infinity) is rational because it can be written as 1/3. And "5" is rational because you can write it as 5/1. But there are some numbers like √2 or π that cannot be written in the a/b form (again, with "a" and "b" being whole numbers), so they're irrational.

An equivalent way to define rational numbers is to say that they're numbers whose decimals either terminate or repeat. So numbers like "5" (which is 5.0) and "-0.25412" have decimals that end at some point, and are therefore rational. 3/11 = 0.27272727.. has a block of repeating decimals that goes on forever, so it's rational. But if you look at √2 = 1.41421356... the decimals look "random".

EDIT: Whenever this question comes up, I see people who say irrational numbers are defined as having decimals that "go on forever". Again, this isn't necessarily true. See the examples above.

Others say that a number is rational if the decimals have a "pattern". Again, this isn't always true. A decimal like "0.18 118 1118 11118 111118..." follows a pattern, but there isn't a block that actually repeats, so this is irrational.

Answer 3

A rational number is a real number that can be expressed in the form:

m / n

for integers m and n.

Irrational numbers are all the other real numbers that aren't rational. Some examples of irrational numbers are π, and the square root of 2.

Answer 4

Rational numbers are those which can be expressed as repeating decimals: this would include all integers and those fractions which have a repeated pattern in their decimal equivalent, Irrational numbers have no such repeated pattern. Classic examples of irrational numbers would be Pi and the square root of 2

Answer 5

This Site Might Help You.

RE:
What is a rational or irrational number?

Answer 6

A rational number is a number that stops it does not keep going. A irrational number is a number that just keeps repeating like pie.

Answer 7

Rational, any number that can be written as a fraction. This includes whole numbers, integers, decimals that terminate(end) or repeat.
examples of rational numbers: 3, -8, 4.6, .2222222......


Irrational, any decimal that does not terminate or repeat. The best example is pi 3.14159.......
Most of them are square root of non - perfect squares
such as the square root of 30

Answer 8

A rational number number can be expressed as a/b where a/b is reduced to its lowest form. An irrational number cannot be so expressed.

Answer 9

a rational number has a repeating pattern
like 1/3 or 1/6
1/3 = 0.3333333333...... (repeating 3)
1/6 = 0.1666666666...... (repeating 6)

a irrational number has no repeating pattern
like pi, or SQRT 2
pi = 3.1415926535897932384626433832795......
SQRT 2 = 1.41421356237309504880168872......