# Standard form addition

To add 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**

Work out the following giving your answer in standard form

`3.8times10^4+8.24times10^5`

## Method 1

Actually carry out the addition

`3.8times10^4+8.24times10^5`

is the same as

`3.8times10times10times10times10` | `+` | `8.24times10times10times10times10times10` |

`38,000` | `+` | `824,000` |

Which is

`824,000` | |

`+` | `ul(38,000)` |

`862,000` |

Convert to standard form

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

Which is `8.62times10^5`

## Method 2

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

`3.8times10^4+8.24times10^5`

and making the powers of `10` the same

`0.38times10^5+8.24times10^5`

Which is

`(0.38+8.24)10^5`

and this equals

`8.62times10^5` (already in standard form)

**Example 2**

Work out the following giving your answer in standard form

`8.04times10^-6+7.63times10^-7`

## Method 1

Is to actually carry out the calculation

`8.04times10^-6+7.63times10^-7`

`=` | `8.04/(10times10times10times10times10times10)` | `+` | `7.63/(10times10times10times10times10times10times10)` |

`=` | `0.00000804` | `+` | `0.000000763` |

`=` | `0.000008040` | ||||||||

`+` | `0.000000763` | ||||||||

`0.000008803` | |||||||||

`1\ \ ` |

`=` | `0.000008803` |

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

But in standard form `=8.803times10^-6`

## Method 2

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

`8.04times10^-6+7.63times10^-7`

Would become

`80.4times10^-7+7.63times10^-7`

`(80.4+7.63)times10^-7`

Which equals

`(88.03)times10^-7`

which is

`88.03times10^-7`

But we need this in standard form

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

is the same as `8.803times10^-6`

**Answer:** is `8.803times10^-6`

**Example 3**

Work out the following giving your answer in standard form

`(8times10^0)+(4.6times10^-3)`

## Method 1

Is to actually carry out an addition calculation

**NOTE:**

any power to zero `=1`

`(8times10^0)` | `+` | `(4.6times10^-3)` |

`(8times1)` | `+` | `(4.6times10^-3)` |

`8` | `+` | `0.0046` |

`=` | `8.0000` | |

`+` | `ul0.0046` | |

`8.0046` |

`=8.0046`

and this is already in standard form

## Method 2

Is actually add up the indices or powers but only if they are the same power.

So change

`(8times10^0)+(4.6times10^-3)`

is

`(8000times10^-3)+(4.6times10^-3)`

which is

`(8000+4.6)times10^-3`

`=8004.6times10^-3`

But we need this in standard form

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

So `8004.6times10^-3`

Becomes `8.0046`

**Answer:** `8.0046`