When adding and subtracting standard form numbers, you have to:

- convert the numbers from standard form into ordinary numbers
- complete the calculation
- convert the number back into standard form

Calculate .

When multiplying and dividing you can use index laws:

- multiply or divide the first part of the numbers
- apply the index laws to the powers of 10
- check whether the first part of the number is between 1 and 10

To multiply powers of 10, add the powers together, eg 10^{6} x 10^{4} = 10^{6 + 4} = 10^{10}. To divide powers of 10, subtract the powers, eg 10^{7} ÷ 10^{2} = 10^{7 - 2} = 10^{5}.

Work out .

Multiply the first numbers – which in this case is .

Apply the index law to the powers of 10:

As 9 is between 1 and 10, this number is in standard form.

Work out .

Multiply the first numbers .

Apply the index law to the powers of 10

28 is not between 1 and 10, so is not in standard form. To convert this to standard form, divide 28 by 10 so that it is a number between 1 and 10. To balance out this out, multiply the second part by 10 which gives 10^{7}.

and are equivalent but only is written in standard form.

So:

- Question
Calculate .

- Divide the first part of the numbers:
- Apply the index laws to the powers of 10
- Check whether the first part of the number is between 1 and 10
- So:

0.25 is not between 1 and 10, so is not in standard form. To convert this to standard form, multiply 0.25 by 10 so that it is a number between 1 and 10. To balance out that multiplication of 10, divide the second part by 10 which gives 10

^{4}. So and are equivalent but only the second is written in standard form.So: