# What is Standard form? And when can I use it?

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Standard form, also referred to as standard index form is a method of writing really big and really small numbers. It uses powers of 10 to express its size.

Standard form is used all the time in science and engineering. It allows you to comprehend numbers with extreme sizes such as the diameter of the sun or the diameter of an atom.

A number in standard form is written like this:

A x 10n

Where:

A is a number that is greater than or equal to 1 and less than 10

n is a positive or negative integer. Where n is positive the starting number is greater than one, where the n is negative the starting number is less than one.

Now let’s try converting a number to standard form and from standard form into an ordinary number. The following two questions are taken from the AQA GCSE foundation specimen paper.

1. Write 2 500 000 in standard form.

First we need to write this as number between 1 and 10 multiplied by a multiple of 10. In this case...

2.5 x 1 000 000

We've found A its 2.5! Now we need to write 1 000 000 in the form 10n as shown

1 000 000 = 10 x 10 x 10 x 10 x 10 x 10 = 106

So the answer is 2.5 x 106

2. Write 1.2 x 10-5 as an ordinary number.

In order to convert from standard for to an ordinary number all we need to do is complete the multiplication.

1.2 x 10-5 = 1.2 x 0.00001 = 0.000015

The main benefit of standard form is that it makes calculations using these numbers significantly easier (this is what we are aiming for). For your exams you will be expected to do this with and without a calculator (eek). This is what we can work on next.

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