# 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`