Standard Form – GCSE Maths Revision and Worksheets

What you need to know:

Standard form is a shorthand developed for expressing numbers that are either very big or very small. You are required to do the following:

• Recognise that any number written like: A \times 10^n is referred to as being in standard form only when the A is bounded by 1 \leq A < 10 and n is a whole number.

• Be able to convert in and out of standard form. This amounts largely to relating the power of 10 (given by n above) to how many times you either have to divide or multiply your number, in order to satisfy the condition of it being greater than or equal to 1 but smaller than 10. For example:

4 \times 10^3 = 4 \times 10 \times 10 \times 10 = 4000.

• Multiply and divide two numbers which are both in standard form. This process involves multiplying/dividing the two initial numbers, and then adding the powers of ten according to the laws of indices. For example:

\left(3 \times 10^8\right) \times \left(5 \times 10^{-6}\right) = 3 \times 5 \times 10^8 \times 10^{-6} = 15 \times 10^2 = 1.5 \times 10^3.

It’s important to note that you may end, as we did here, with a number not in standard form. You will lose a mark if you leave your answer like this, so make sure that the initial actually does fall between 1 and 10.