Calculations in standard index form

Multiplying and dividing numbers in standard form

Here you can use the rules for multiplying and dividing powers. Remember these rules:

  • To multiply powers you add, eg {10}^{5} \times {10}^{3} = {10}^{8}
  • To divide powers you subtract, eg {10}^{5} \div {10}^{3} = {10}^{2}


Simplify (2 \times {10}^{3}) \times (3 \times {10}^{6}).


It is useful to separate the numbers and the indices, and then multiply the {2} by {3} and add the powers of {10}:



A similar method is used when dividing:


Simplify (6\times10^4)\div(2\times10^2).


Another way to write a division is to write it in the form of a fraction. The numbers and the indices can then be separated, before dividing the {6} by {2} and subtracting the powers of {10}:




Simplify (8.4\times10^5)\div(4\times10^3).

Did you get 2.1\times{10}^{2}?

Remember to write the division in the form of a fraction to start.


Remember you should first work out {8.4}\div{4}, then subtract the powers of {10} (because it is division), like this:


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