# Standard form subtraction

To subtract in standard form all you need to remember is

Make the powers of `10` the same

**NOTE:**

To make the power of `10` the same remember

`0.001`

is the same as `0.01times10^-1` (Move decimal right and `-1` to the power)

is the same as `0.1times10^-2` (Move decimal right again and `-1` to the power again)

is the same as `1.0times10^-3` (Standard form)

is the same as `0.0001times10^1` (Move decimal left and `+1` to the power)

is the same as `0.00001times10^2` (Move decimal left again and `+1` to the power again)

**Example 1**

Calculate the following giving your answer in standard form

`6.2times10^-5-5.06times10^-7`

## Method 1

Actually carry out the subtraction

`6.2times10^-5-5.06times10^-7`

is the same as:

`6.2/(10times10times10times10times10)-5.06/(10times10times10times10times10times10times10)`

Which is

`0.000062-0.000000506`

which is

`0.000062000` | |

`-` | `0.000000506` |

`0.000061494` |

remember move decimal place to right and `-1` to the power.

or `6.1494times10^-5`

## Method 2

An alternative way is to add the indices but you need to make the powers the same.

`6.2times10^-5-5.06times10^-7`

Make the power of `10` the same

remember move the decimal place to the right and `-1` to the power

So this calculation is the same as `620times10^-7-5.06times10^-7`

which is `(620-5.06)times10^-7`

`614.94times10^-7`

Now put this in standard form

remember move decimal place to the left and `+1` to the power.

`6.1494times10^-5`

**Example 2**

Calculate the following giving your answer in standard form

`(8.73times10^8)-(2.18times10^5)`

## Method 1

Actually carry out the subtraction

`(8.73times10^8)-(2.18times10^5)`

is the same as

`8.73times10times10times10times10times10times10times10times10-2.18times10times10times10times10times10`

which is

`873,000,000-218,000`

which is

`1` | `1` | `1` | ||||||||

`=` | `8` | `7` | `3,` | `0` | `0` | `0,` | `0` | `0` | `0` | |

`1` | `3` | `2` | ||||||||

`-` | `cancel2` | `cancel1` | `8,` | `0` | `0` | `0` | ||||

`8` | `7` | `2,` | `7` | `8` | `2,` | `0` | `0` | `0` |

But in standard form this is

`8.72782times10^8`

## Method 2

An alternative way is to subtract indices but you need to make the powers of `10` the same.

`8.73times10^8-2.18times10^5`

is the same as

`8.73times10^8-0.00218times10^8`

Now because the powers are the same we can subtract

`8.73times10^8-0.00218times10^8`

is `(8.73-0.00218)times10^8`

`(8.72782)times10^8`

`=8.72782times10^8`

Which is already in standard form.

**Example 3**

Calculate the following giving your answer in standard form

`(3.62times10^-8)-(6.14times10^-10)`

## Method 1

Actually carry out the subtraction

`(3.62times10^-8)-(6.14times10^-10)`

is the same as

`3.62/(10times10times10times10times10times10times10times10)`

`-6.14/(10times10times10times10times10times10times10times10times10times10)`

which is

`0.000,000,036,2-0.000,000,000,614`

which is

`1` | `1` | `1` | ||||||||||||

`=` | `0.` | `0` | `0` | `0,` | `0` | `0` | `0,` | `0` | `3` | `6,` | `2` | `0` | `0` | |

`1` | `7` | `2` | ||||||||||||

`-` | `0.` | `0` | `0` | `0,` | `0` | `0` | `0,` | `0` | `0` | `cancel0,` | `cancel6` | `cancel1` | `4` | |

`0.` | `0` | `0` | `0,` | `0` | `0` | `0,` | `0` | `3` | `5,` | `5` | `8` | `6` |

Now put in standard form

remember move decimal to the right and `-1` to the power

`3.5586times10^-8`

## Method 2

`(3.62times10^-8)-(6.14times10^-10)`

Subtract using indices but first make the power of `10` the same

remember move the decimal place to the right and `-1` to the power

So `362times10^-10=3.2times10^-8`

therefore the calculation becomes

`362times10^-10-6.14times10^-10`

`(362-6.14)times 10^-10`

`=355.86times10^-10`

Now put in standard form

remember move the decimal to the left and `+1` to the power

`3.5586times10^-8`