Types of Number (Cambridge (CIE) IGCSE Maths: Core): Revision Note

Types of number

You will come across vocabulary such as

• Integers and natural numbers

• Rational and irrational numbers

• Multiples

• Factors

• Prime numbers

• Squares, cubes and roots

• Reciprocals

Knowing what each of these terms mean is essential.

What are integers and natural numbers?

• Integers are whole numbers;

  • They can be positive, negative and zero

  • For example, -3, -2, -1, 0, 1, 2, 3  are all integers

• Natural numbers are the positive integers

  • They can be thought of as counting numbers

  • 1, 2, 3, 4, … are the natural numbers

    • Notice that 0 is not included

What are rational and irrational numbers?

• A rational number is a number that can be written as a fraction in its simplest form

  • A rational number can be written in the form $\frac{a}{b}$

    • where $a$ and $b$ are both integers, and $b$ is not zero

  • All terminating decimals are rational numbers

    • e.g. $0.32=\frac{32}{100}$

  • All recurring decimals are rational numbers

    • e.g. $0.4444...=\frac{4}{9}$ 

    • Recurring digits are indicated by dots or bars
      e.g.  $0.4\dot{5}=0.4\overline{5}=0.455555555...$ 
      e.g.  $0.\dot{5}82\dot{4}=0.\overline{5824}=0.582458245824...$

• An irrational number cannot be written as a fraction

  • All non-terminating, non-recurring decimals are irrational numbers

  • $\pi$ (pi) is an irrational number

    • It has an endless amount of decimal places and there is no pattern or recurring digits

    • Any (simplified) fraction involving $\pi$, such as$\frac{\pi }{2}$, will also be irrational (as $a$ in $\frac{a}{b}$ is not an integer)