What are irrational and rational numbers?

Answer 1

Rational numbers are any numbers that can be expressed as a fraction. For example 1/3, 1/2, and 2. Irrational Numbers are numbers that can not be expressed as a fraction. Some examples are Pi, the square root of 2, and e. Both rational and irrational numbers are real numbers. Unlike imaginary numbers like the square root of -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.
Rational and irrational numbers are both subsets of real numbers, together they make up the set of what we call real numbers.

If you have trouble remembering which is which, just think of rational numbers as fractions, or numbers that can be written as a/b where a and b are integers. Remember that b can equal 1 so [2 = 2/1]. Therefore all integers, as well as whole and natural numbers are also rational numbers.

Irrational numbers are real numbers that are not rational. One way that people describe Irrational is the answer goes on and on forever and does not have a repeating pattern. Two classic examples are Pi (3.14159...), and the base of the natural log e (2.7128...).

Rational, when expressed in decimal form, can stop (terminate) at a certain point or it may have a pattern of digits which repeats forever. An example of a rational that repeats is 1/3. Certainly it is written as a/b with a and b both being integers, but its decimal representation is 0.333.... where in this case the dots mean that the (3) repeats forever.

There is a hierarchy of numbers and understanding it sometimes helps remember and understand the differences.

At the top of the hierarchy are the complex numbers. Next come the real numbers and then then rational numbers. Next comes the integers, then the whole numbers and last the natural numbers.
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.

Answer 2

A rational number can be expressed as a fraction a/b, where a and b are integers. This includes the integers themselves, that can be expressed as (number) / 1.

An irrational number is one that can't be exactly expressed in this way. This includes the square roots of any integer that is not a perfect square; pi; and e - and a host of other numbers. There are more rational than irrational numbers (rational numbers are a countable infinity", and irrational numbers an "uncountable infinity"), but we usually deal mainly with rational numbers - or use rational approximations for the numbers we deal with.

Answer 3

A rational number is a real number that can be expressed in the form of a ratio of two integers, the second of which is not zero. An irrational number is a real number that cannot be expressed in that form.

Answer 4

A rational number can be expressed as a ratio of two integers, an irrational number cannot be so expressed.

Answer 5

In mathematics, a rational number is one that can be expressed as a ratio of two integers whereas an irrational number is a real number which cannot be so expressed.

Answer 6

Rational numbers can be expressed as a ratio of two integers (the second being non-zero). Irrational numbers cannot be expressed in that way.