Standard form multiply
To multiply in standard form all you need to remember is that
102=10×10=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
(3.7×104)×(5.21×105)
Method 1
Actually carry out the multiplication
(3.7×104)×(5.21×105)
is the same as
3.7×10×10×10×10×5.21×10×10×10×10×10
and the same as
3.7×5.21×109
which is the same as
19.277×109
But this is not in standard form so
19.277×109
in standard form is
and remember move decimal left and +1 to the power
Answer: is 1.9277×1010
Method 2
An alternative way to calculate this is to say what is a simpler calculation.
What is
102×102=10×10×10×10=10,000
or 104
So 102×102=102+2=104
Therefore
3.7×5.21×104×105
Is the same as
3.7×5.21×104+5
=3.7×5.21×109
=19.277×109
and again change this to standard form
and remember move decimal left and +1 to the power
=1.927×1010
Example 2
Work out the following giving your answer in standard form
(6.3×100)×(6.3×103)
Method 1
Actually carry out the multiplication
NOTE:
any number to the power zero is 1
So this becomes
6.3×6.3×10×10×10
=39.69×10×10×10
=39,690
remember move decimal left and +1 to the power
So in standard form this =3.969×104
Method 2
An alternative method is to calculate using indices but first find a simple example we know.
We know
102×102=10×10×10×10=10,000
which is the same as
102×102=102+2=104
Therefore
6.3×100×6.3×103
=6.3×6.3×100×103
=6.3×6.3×103+0
=6.3×6.3×103
=39.690×103
But in standard form this equals
and remember move decimal left and +1 to the power
3.969×104
Example 3
Work out the following giving your answer in standard form
(3.2×10-5)×(7×107)
Method 1
Actually carry out the multiplication
(3.2×10-5)×(7×107)
is the same as
(3.210×10×10×10×10)×(7×10×10×10×10×10×10×10)
(0.000032)×(70,000,000)
=2240
and in standard form this is
remember move decimal left and +1 to the power
2.24×103
Method 2
An alternative way is to calculate this using indices but first find a simple example we know as follows:
10-2×103
=110×10×10×10×10
=10×10×1010×10
=10
is the same as 10-2×103
=10-2+3
=101
=10
So the real calculation is
(3.2×10-5)×(7×107)
is the same as 3.2×10-5×7×107
=3.2×7×107×10-5
=3.2×7×107-5
=3.2×7×102
=22.4×102
remember move decimal left and +1 to the power
So in standard form this is 2.24×103
