 # 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

(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

(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

(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