P a g e
 3
Note that
3,560,000,000
3.56
1,000,000,000
=
But if we divide by 1,000,000,000 we must also multiply by
1,000,000,000 or the value of the number will be changed.
But
1,000,000,000 = 10
9
Therefore
: 3,560,000,000 =
9
9
3,560,000,000
10
3.56 10
1,000,000,000
x
x
=
Example 2:
Convert 0.000000123 to scientific notation.
Note that 0.000000123 * 10,000,000 = 1.23
But if we multiply by 10,000,000 we must also divide by
10,000,000 or the value of the number will be changed.
But 10,000,000 = 10
7
7
7
7
0.000000123 10,000,000
1.23
0.000000123
1.23 10
10
10
x
x

∴
=
=
=
Naturally, we don’t want to go through these laborious
processes every time we want to convert from decimal to
scientific notation, so:
Rule 1:
For numbers >1, move the decimal point to the left
until it falls just to the right of the 1
st
nonzero digit.
Then multiple by 10
n
where n = the number of places the
decimal point was moved.
Rule 2:
For numbers <1, move the decimal point to the
right until it falls just to the right of the 1
st
nonzero
digit. Then multiple by 10
n
where n = the number of places
the decimal point was moved.
D. Doing Calculations with numbers written in scientific
notation:
One reason that scientific
notation is so
popular with scientists is that using it greatly simplifies
doing quick calculations.
However to do this, we must
abide by a couple of rules.