Classify numbers

key notes :

Classifying Numbers

Classifying numbers involves understanding the different types of numbers and their properties. Here’s a breakdown of the main types of numbers and how to classify them:

Natural Numbers(N)

  • Definition: Numbers that are used for counting and ordering. They start from 1 and go on infinitely.
  • Examples: 1, 2, 3, 4, 5, 6, 7, …

Note: Natural numbers do not include zero or negative numbers.

Whole Numbers (w)

  • Definition: Natural numbers plus zero.
  • Examples: 0, 1, 2, 3, 4, 5, 6, …

Note: Whole numbers include zero but not negative numbers or fractions.

Integers (I)

  • Definition: All whole numbers and their negative counterparts.
  • Examples: -3, -2, -1, 0, 1, 2, 3, …

Note: Integers include positive numbers, negative numbers, and zero.

Rational Numbers (Q)

  • Definition: Numbers that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero.
  • Examples: 1/2, -3/4, 5, 0.75 (since 0.75 = 3/4)

Note: All integers, fractions, and finite or repeating decimals are rational numbers.

Irrational Numbers (Q’)

  • Definition: Numbers that cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal parts.
  • Examples: √2, π (pi), e

Note: Irrational numbers have infinite decimal expansions that do not repeat.

Real Numbers (R)

  • Definition: All the numbers that can be found on the number line, including both rational and irrational numbers.
  • Examples: -2, 0, 3.14, √5, π

Note: Real numbers include all rational and irrational numbers.

Prime Numbers

  • Definition: Natural numbers greater than 1 that have exactly two distinct factors: 1 and themselves.
  • Examples: 2, 3, 5, 7, 11, 13

Note: The number 2 is the only even prime number.

Composite Numbers

  • Definition: Natural numbers greater than 1 that have more than two factors.
  • Examples: 4, 6, 8, 9, 10, 12

Note: Composite numbers can be factored into smaller natural numbers.

Even Numbers

  • Definition: Numbers divisible by 2.
  • Examples: -4, 0, 2, 6, 8, 10

Note: Even numbers end in 0, 2, 4, 6, or 8.

Odd Numbers

  • Definition: Numbers not divisible by 2.
  • Examples: -3, 1, 5, 7, 9

Note: Odd numbers end in 1, 3, 5, 7, or 9.

Absolute Value

  • Definition: The distance of a number from zero on the number line, regardless of direction.
  • Examples: |3| = 3, |-5| = 5

Note: The absolute value of a number is always a non-negative number.

Learn with an example

Is 5.666… a whole number?

  • yes
  • no

Whole numbers are counting numbers and 0. So, 5.666… is not a whole number.

Which of the following describe 1/9? Select all that apply.

  • integer
  • whole number
  • rational number
  • real number

Whole numbers are counting numbers and 0. So, 1/9 is not a whole number.

Integers are counting numbers, their opposites, and 0. So, 1/9 is not an integer.

1/9 is a fraction. So, 1/9 is a rational number.

Since real numbers include rational numbers, 1/9 is also a real number.

There are two correct answer choices. 1/9 is a rational number and a real number.

Which of the following describe 0? Select all that apply.

  • integer
  • whole number
  • irrational number
  • rational number

Whole numbers are counting numbers and 0. So, 0 is a whole number

Integers are counting numbers, their opposites, and 0. So, 0 is an integer.

0 can be written as 0/1 , which is a fraction. So, 0 is a rational number

Since 0 is a rational number, it is not an irrational number.

There are three correct answer choices. 0 is a whole number, an integer, and a rational number.

let’s practice!