# Standard form

Standard form is way of expressing numbers that are either very large or too small to use. Take for example the number;

1,000,000,000,000,000,000,000,000

This is such a very huge number to read or write. It would be incredibly hard to use in any maths calculation and you wouldn’t be able to enter such a number in a calculator. It is also very hard to remember! You would have to find some easy way to write it and this is where you use standard form. The above number can be written as;
10

As you can see the number is very easy to remember and it would be easy to use in any maths calculation since it has a few digits.
^{24}0.00000000000000000000000009

Similarly with the above number it is just too small to work with, it has too many numbers of 0s and looks to busy to remember. The above number can be written as;
9 x 10

Here are some examples of standard forms, try to observe the pattern.
^{-27}Standard form | …means | Actual value |
---|---|---|

2 x 10^{3} | 2 x 10 x 10 x 10 | 2000 |

2 x 10^{2} | 2 x 10 x 10 | 200 |

2 x 10^{1} | 2 x 10 | 20 |

2 x 10^{0} | 2 x 1 | 2 |

2 x 10^{-1} | 2 x 0.1 | 0.2 |

2 x 10^{-2} | 2 x 0.1 x 0.1 | 0.02 |

2 x 10^{-3} | 2 x 0.1 x 0.1 x 0.1 | 0.002 |

## Work out example

**Convert 40,000 into standard form.**40,000 = 4 x 10,000*…we know that;*10,000 = 10^{4}*…this means that;*40,000 = 4 x 10^{4}When writing numbers into standard form you must remember this very important rule;The first number must always be a number between 1 and less than 10 but not 10.

**Write 450,000 in standard form***Note there is a difference between this question and the above question.*450,000 = 4.5 x 10,0000*…we understand that;*10,0000 = 10^{5}*…this means;*450,000 = 4.5 x 10^{5}## Work out example 2

Write 0.0000006 in standard form 0.0000006 = 6 x 0.0000001*…we know that;*0.0000001 = 10^{-7}*…this means;*0.0000006 = 6 x 10^{-7}Convert 0.000434 to standard form.*You have to remember that the first number is always less that 10 (positive)*0.000434 = 4.34 x 0.0001*…we understand that;*0.0001 = 10^{-4}*…this should mean;*0.000434 = 4.34 x 10^{-4}You must always remember when working with standard forms that the first number is always between 1 and less than 10

For example; 13 x 10^{4}is not in standard form, neither is 0.13 x 10^{-3}. The true standard form is;**1.3 x 10**or^{4}**1.3 x 10**. Notice the first number is between 1 and less than 10. You must always watch out for that!^{-3}