Standard Form (Edexcel GCSE Maths: Foundation)

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
• 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
• 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 multiply or divide two numbers in standard form?

• If you can, use a calculator!
• Otherwise multiply/divide the number parts first
  
  • If this answer is less than 1 or 10 or more then you will need to write it in standard form again
    • 4 × 5 = 20 = 2 × 10¹
    • 2 ÷ 4 = 0.5 = 5 × 10^-1
• Then multiply/divide the powers of 10 using the laws of indices
• Multiply the two parts together to get your answer in standard form
  • You might have to use the laws of indices once more
    • 4 × 10² × 5 × 10⁷
    • = 2 × 10¹ × 10⁹
    • = 2 × 10¹⁰

How do I add or subtract two numbers in standard form?

• If you can, use a calculator!
• If the two numbers have the same power of 10 then you can simply add/subtract the number parts
  • If the answer is less than 1 or 10 or more then you will have to rewrite in standard form
    • 7 × 10⁵ - 6.2 × 10⁵
    • = 0.8 × 10⁵
    • = 8 × 10^-1 × 10⁵
    • = 8 × 10⁴ 
• Otherwise convert both numbers so that they have the same power of 10
  • Choose the larger power
    • 7 × 10⁵ + 6 × 10⁴
    • = 7 × 10⁵ + 0.6 × 10⁵
    • = 7.6 × 10⁵
• If the powers of 10 are small then you might find it easier to convert both numbers to ordinary numbers before adding/subtracting
  • You can convert your answer back to standard form if needed

How do I find powers of a number in standard form?

• If you can, use a calculator!
• As standard form is two terms multiplied together you can split the power
  • Raise the number part to the power
  • Multiply the power of 10 by the new power
    • (3 × 10⁵)²
    • 3² × (10⁵)²
    • 9 × 10¹⁰

• Check to see whether you have to write your final answer in standard form