Standard Form (CIE IGCSE Maths: Core)

What is standard form and why is it used?

• Standard form is a way of writing very large and very small numbers using powers of 10
• This allows us to:
  • Write them more concisely
  • Compare them more easily
  • Perform calculations with them more easily

How do I write a number in standard form?

• Numbers written in standard form are always written as:

• Where:
  • ( is between 1 and 10)
  • ( is positive) for large numbers
  • ( is negative) for small numbers

How do I write a large number in standard form?

• To write a large number such as 3 240 000 in standard form
  • Identify the value of
    • 3.24
  • Find how many times you must multiply 3.24 by 10, to make 3 240 000
    • Count how many places you need to move the decimal point
    • We need to multiply by 10 six times
  • 3 240 000 = 3.24 × 10 × 10 × 10 × 10 × 10 × 10 = 3.24 × 10⁶

How do I write a small number in standard form?

• To write a small number such as 0.000567 in standard form
  • Identify the value of
    • 5.67
  • Find how many times you must divide 5.67 by 10, to make 0.000567
    • Count how many places you need to move the decimal point
    • We need to divide by 10 four times
    • We are dividing rather than multiplying so the power will be negative
  • 0.000567 = 5.67 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 5.67 × 10^-4

How do I perform calculations with numbers in standard form?

• Your calculator can be used to help you carry out calculations with numbers written in standard form
• Make use of brackets around each number, and use the  button to enter numbers in standard form
  • e.g.  
  • You can instead use the standard multiplication and index buttons
• If the answer produced by your calculator is not in standard form, but the answer requires it:
  
  • Either rewrite it using the standard process
    • e.g. 3 820 000 = 3.82 × 10⁶
  • Or rewrite  in standard form, then apply the laws of indices
    
    • e.g.  243 × 10²⁰ = (2.43 × 10²) × 10²⁰ = 2.43 × 10²²