Irrational Numbers
Irrational (not rational) numbers are real numbers which cannot be written as a fraction of two integers.
An irrational number has an infinite number of digits after the decimal point. Unlike 0.3̅, these digits do not form a repeating pattern. A well-known irrational number is pi (π), which is approximately 3.1415926535... . Irrational numbers also include the square root of any number that is not a perfect square. There are infinitely many irrational numbers.
Real Numbers
The set of real numbers contains all of the following:
- Natural Numbers
- Whole Numbers
- Integers
- Rational Numbers
- Irrational Numbers
The real numbers form the real number line. There are infinitely many real numbers.
Integers
Integers are the natural numbers, their negatives, and zero.
... -3, -2, -1, 0, 1, 2, 3, ...
There are infinitely many integers.
Whole Numbers
Whole numbers are the set of all natural numbers in addition to the number 0.
0, 1, 2, 3, 4, 5, 6, ...
There are infinitely many whole numbers.
Rational Numbers
A rational number is a number that can be written as a fraction, or ratio, of two integers.
For example, 1.5 can be written as a ratio of the two integers 3 and 2.
1.5 =
Rational numbers include decimals that terminate or repeat, as they can be written as a ratio of two integers. There are infinitely many rational numbers.
Natural Numbers
Also called counting numbers, natural numbers are the numbers used for counting things.
1, 2, 3, 4, 5, 6, ...
There are infinitely many natural numbers.
The Real Number System
Jacob Kenison
Created on May 15, 2024
Interactive diagram giving a general overview of the different number sets in the real number set.
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Transcript
Irrational Numbers
Irrational (not rational) numbers are real numbers which cannot be written as a fraction of two integers.
An irrational number has an infinite number of digits after the decimal point. Unlike 0.3̅, these digits do not form a repeating pattern. A well-known irrational number is pi (π), which is approximately 3.1415926535... . Irrational numbers also include the square root of any number that is not a perfect square. There are infinitely many irrational numbers.
Real Numbers
The set of real numbers contains all of the following:
The real numbers form the real number line. There are infinitely many real numbers.
Integers
Integers are the natural numbers, their negatives, and zero.
... -3, -2, -1, 0, 1, 2, 3, ...
There are infinitely many integers.
Whole Numbers
Whole numbers are the set of all natural numbers in addition to the number 0.
0, 1, 2, 3, 4, 5, 6, ...
There are infinitely many whole numbers.
Rational Numbers
A rational number is a number that can be written as a fraction, or ratio, of two integers.
For example, 1.5 can be written as a ratio of the two integers 3 and 2.
1.5 =
Rational numbers include decimals that terminate or repeat, as they can be written as a ratio of two integers. There are infinitely many rational numbers.
Natural Numbers
Also called counting numbers, natural numbers are the numbers used for counting things.
1, 2, 3, 4, 5, 6, ...
There are infinitely many natural numbers.