To convert from decimal to scientific
notation for a number greater than 10,
start at the location where the decimal
point actually is
or where it would be, which is to the
right of the ones place.
Then move the decimal point to the left
until it lands between the first two
numbers.
We move the decimal point three places
so our exponent will be three.
When we write this number in scientific
notation it becomes one point two
three one times ten to the three.
For a number between 0 and 1, start at
the location where the decimal point
is. Then move the decimal point to the
right
until it lands between the first two
non-zero digits,
which in this case is the one and the
two.
We move the decimal point three places
so the value of our exponent will be a
three,
and the sign will be negative because
the number is between zero and one.
When we write this number in scientific
notation it becomes one point two three
one
times ten to the negative three.
When converting from scientific to
decimal notation,
first look at the exponent. This
numerical value
equals the total factors of 10 we have
to consider.
Then start at the decimal point and move
it this number of places to the right,
if possible. Here we were only able to
move
three places, which means we need one
more place
or one added zero to equal the four
total factors shown by the exponent.
When we write this number in decimal
notation
it becomes one two three one zero.
Without a terminal decimal point there
are four significant figures,
which is how many were expressed in the
original scientific notation.
We are converting from scientific
notation, so we look at the value of the
exponent.
This numerical value equals the total
factors of 10 we have to consider,
which for this example is 5. Because the
sign of the exponent is negative,
we start at the decimal point and move
it one place to the left,
which will always be our only option.
The value of the exponent here is
greater than one, so we have to move it
over
four more places to equal the
five factors of ten shown by the
exponent.
When we write our decimal notation, we
start
with a leading zero and a decimal point,
then our four added zeros, and get zero
point
zero zero zero zero one two
three one.
