Mammoth Memory

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

So this calculation is the same as 

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

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`

 

 

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