1.1.1 Standard Form

Standard form (sometimes called scientific notation or standard index form) gives us a way of writing very big and very small numbers using powers of 10.

Why use standard form?

• Some numbers are too big or too small to write easily or for your calculator to display at all
  • Imagine the number 50⁵⁰ , the answer would take 84 digits to write out
  • Try typing 50⁵⁰ into your calculator, you will see it displayed in standard form
• Writing very big or very small numbers in standard form allows us to:
  • Write them more neatly
  • Compare them more easily
  • Carry out calculations more easily
• Exam questions could ask for your answer to be written in standard form

How is standard form written?

• In standard form numbers are always written in the form where and satisfy the following conditions:
  • 
    • So there is one non – zero digit before the decimal point
  •  
    • So must be an integer
  • for large numbers
    • How many times is multiplied by 10
  • for small numbers
    • How many times is divided by 10

How are calculations carried out with standard form? 

• Your GDC will display large and small numbers in standard form when it is in normal mode
  • Your GDC may display standard form as aEn
    • For example,  will be displayed as
    • If so, be careful to rewrite the answer given in the correct form, you will not get marks for copying directly from your GDC
• Your GDC will be able to carry out calculations in standard form
  • If you put your GDC into scientific mode it will automatically convert numbers into standard form
    • Beware that your GDC may have more than one mode when in scientific mode
    • This relates to the number of significant figures the answer will be displayed in
    • Your GDC may add extra zeros to fill spaces if working with a high number of significant figures, you do not need to write these in your answer
• To add or subtract numbers written in the form without your GDC you will need to write them in full form first
• To multiply or divide numbers written in the form without your GDC you can either write them in full form first or use the laws of indices