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

Which is

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`

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`

`=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`