Standard form multiply
To multiply in standard form all you need to remember is that
`10^2=10times10=100`
NOTE:
See indices Mammoth memory for further explanation
But the basis of multiply 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
`(3.7times10^4)times(5.21times10^5)`
Method 1
Actually carry out the multiplication
`(3.7times10^4)times(5.21times10^5)`
is the same as
`3.7times10times10times10times10times5.21times10times10times10times10times10`
and the same as
`3.7times5.21times10^9`
which is the same as
`19.277times10^9`
But this is not in standard form so
`19.277times10^9`
in standard form is
and remember move decimal left and `+1` to the power
Answer: is `1.9277times10^10`
Method 2
An alternative way to calculate this is to say what is a simpler calculation.
What is
`10^2times10^2=10times10times10times10=10,000`
or `10^4`
So `10^2times10^2=10^(2+2)=10^4`
Therefore
`3.7times5.21times10^4times10^5`
Is the same as
`3.7times5.21times10^(4+5)`
`=3.7times5.21times10^9`
`=19.277times10^9`
and again change this to standard form
and remember move decimal left and `+1` to the power
`=1.927times10^10`
Example 2
Work out the following giving your answer in standard form
`(6.3times10^0)times(6.3times10^3)`
Method 1
Actually carry out the multiplication
NOTE:
any number to the power zero is `1`
So this becomes
`6.3times6.3times10times10times10`
`=39.69times10times10times10`
`=39,690`
remember move decimal left and `+1` to the power
So in standard form this `=3.969times10^4`
Method 2
An alternative method is to calculate using indices but first find a simple example we know.
We know
`10^2times10^2=10times10times10times10=10,000`
which is the same as
`10^2times10^2=10^(2+2)=10^4`
Therefore
`6.3times10^0times6.3times10^3`
`=6.3times6.3times10^0times10^3`
`=6.3times6.3times10^(3+0)`
`=6.3times6.3times10^3`
`=39.690times10^3`
But in standard form this equals
and remember move decimal left and `+1` to the power
`3.969times10^4`
Example 3
Work out the following giving your answer in standard form
`(3.2times10^-5)times(7times10^7)`
Method 1
Actually carry out the multiplication
`(3.2times10^-5)times(7times10^7)`
is the same as
`(3.2/(10times10times10times10times10))times(7times10times10times10times10times10times10times10)`
`(0.000032)times(70,000,000)`
`=2240`
and in standard form this is
remember move decimal left and `+1` to the power
`2.24times10^3`
Method 2
An alternative way is to calculate this using indices but first find a simple example we know as follows:
`10^-2times10^3`
`=1/(10times10)times10times10times10`
`=(10times10times10)/(10times10)`
`=10`
is the same as `10^-2times10^3`
`=10^(-2+3)`
`=10^1`
`=10`
So the real calculation is
`(3.2times10^-5)times(7times10^7)`
is the same as `3.2times10^-5times7times10^7`
`=3.2times7times10^7times10^-5`
`=3.2times7times10^(7-5)`
`=3.2times7times10^2`
`=22.4times10^2`
remember move decimal left and `+1` to the power
So in standard form this is `2.24times10^3`
