Types of Numbers | Mathematics for Grade 10 PDF Download

What are Types of Numbers?

Types of numbers are different sets of numerical values.
To determine the type of number, you must use the definition to see whether the number belongs to the set.

Understand number definitions and terms

A number is a count or measurement.
We write or talk about numbers using numerals such as ‘6’. We need to know the different types of numbers to be able to solve problems.

• Positive and negative numbers
  Any number above zero is a positive number and any number below zero is a negative number.
  
• Real Numbers
  All numbers on a number line are real numbers.
  Real numbers can also be classified as rational or irrational.
• Rational and irrational numbers
  We can make a rational number by dividing an integer by an integer.
  Irrational numbers are the real numbers that cannot be expressed in fraction form.
• Natural numbers are positive integers (including 00). We can also call these ‘counting’ numbers’.

For example,

• Even and odd
  Even numbers are divisible by 2 without remainders; they end in 2, 4, 6 or 8.
  Odd numbers are not divisible by 2 without remainders and end in 1, 3, 5, 7 or 9.
  For example,
• Decimals 
  We can recognise decimal numbers because they have a whole number and a fractional part. The decimal point separates the whole number from the fractional part.
  For example,
  
• Prime numbers and composite numbers
  A prime number is a number which is only divisible by 1 and itself. We can define composite numbers as whole numbers that have more than two factors.
  For example,
  3 = 3 × 1, so 3 is prime.
  6 = 3 × 2, or 6 = 1 × 6. 6 has more than two factors, so 6 is composite.
  We also need to recognise the properties of some other ‘special’ numbers.
• Square numbers
  Square numbers are the product of a number that has been multiplied by itself.
  We can show square numbers using a pattern of dots in a square.
  For example,
• Cube numbers
  A Cube number is the product when a number has been multiplied by itself twice. We can show cube numbers using 3D cubes.
  For example,
  

• Triangular numbers
  A Triangular number is a number that can be shown using a pattern of dots in an equilateral triangle. We can find a triangular number by cumulatively adding natural numbers.
  For example,
  
• Reciprocal maths
  A reciprocal of a number is its multiplicative inverse. This means that if you multiply a number by its reciprocal the answer is 1.
  To find a reciprocal you divide 11 by the number.
  For example, the reciprocal of 3 is 1/3

Key Types of Number

Below is a description of each of these types of numbers, along with a few examples.

Other Types of Number

Fractions and Decimals

There are also a few specific types of numbers involving fractions and decimals that you are expected to understand. Below is a table outlining these different types of fractions and decimals.