Mammoth Memory

Standard form divide

To divide in standard form all you need to remember is that

Division of standard form formula

NOTE:

See indices Mammoth memory for further explanation

 

But the basis of divide in standard form is first look for a simple comparable that you know with indices.

i.e. try simple numbers you know first

 

Example 1

Work out the following giving your answer in standard form

`44800div6.4times10^9`

 

Method 1

Actually carry out the division

`44800div6.4times10^9`

is the same as

`44800div6.4times10times10times10times10times10times10times10times10times10`

which is

`44800div640,000,000`

which is

`(448cancel0cancel0)/(6400,000,0cancel0cancel0)`

`448/(64,000,000)`

`=0.000007`

and to put this in standard form

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

Answer: is `=7times10^-6`

 

Method 2

An alternative way to calculate this is to say what is a simpler calculation, what is

`10^2div10^3`

`=(cancel10timescancel10)/(10timescancel10timescancel10)=1/10`

`=10^-1`

Therefore

`44800div6.4times10^9`

is the same as

`4.48times10^4div6.4times10^9`

`(4.48times10^4)/(6.4times10^9)`

`4.48/6.4times10^4/10^9`

`0.7times10^-5`

and in standard form this is

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

Answer: is `7times10^-6`

 

Example 2

Work out the following giving your answer in standard form

`(1.4times10^12)div(3.2times10^4)`

 

Method 1

Actually carry out the division

`1.4times10^12=1.4times10times10times10times10times10times10`

`times10times10times10times10times10times10`

`=1,400,000,000,000`

and

  `3.2times10^4=3.2times10times10times10times10`

`=32,000`

So the calculation becomes

`(1,400,000,000,cancel(000))/(32,cancel(000))`

`=(1,400,000,000)/32`

`=43,750,000`

and to put this in standard form

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

Answer is `=4.357times10^7`

 

Method 2

An alternative way to calculate this is to say what is a simpler calculation, what is

`10^2div10^3`

 `=(cancel10timescancel10)/(10timescancel10timescancel10)=1/10=10^-1`

Therefore:

`(1.4times10^12)div(3.2times10^4)`

is the same as

`(1.4times10^(cancel(\ 12)8))/(3.2timescancel10^cancel(\ 4))`

`(1.4times10^8)/3.2`  

 `=0.4375times10^8`

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

and to put this in standard form this becomes

`4.375times10^7`

 

Example 3

Work out the following giving your answer in standard form

`3.8times10^8div1.9times10^-3`

 

Method 1

Actually carry out the division

`3.8times10^8div1.9times10^-3`

is the same as

`3.8times10times10times10times10times10times10times10times10div1.9/(10times10times10)`

which is

`380,000,000div0.0019`

which is

`(380,000,000)/0.0019`

`=200,000,000,000`

and to put this in standard form

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

Answer: is `2times10^11`

 

Method 2

An alternative is to find a similar calculation that you know. In this case

`10^2div10^-2`

`=1000div0.1`

`=1000/0.1=10,000`

or similarly

`10^2div10^-2`

is

`10^2div1/10^2`

`=10^2/(1/10^2)`

`=10^2times10^2`

`=10^4`

`=10,000`

Now to the actual calculation

`3.8times10^8div1.9times10^-3`

would be

`3.8times10^8div1.9/10^3`

`=(3.8times10^8)/(1.9/10^3)`

`=(3.8times10^8times10^3)/1.9`

`=(3.8times10^11)/1.9`

`=2times10^11`

which is already in standard form so the answer is `=2times10^11`

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