Scientific notation is a value written as a
simple number multiplied by a power of
ten. It is another way of writing numbers. It
also makes calculating these numbers
Correct scientific notation has a coefficient
that is less than 10 and greater than or
equal to 1. That coefficient is then multiplied
by a power of ten.
46000 = 4.6 x 104
The steps for writing scientific
notation are rather simple. Let's
go over them by actually changing
numbers into scientific notation.
The distance between Earth and
Neptune is 4,600,000,000,000
meters. How do we write it in
Place the decimal point after the
first whole number digit and
drop the zeros. The number "4"
is the first whole number.
Find the exponent. To do this, count the
number of places from the new
decimal point to the end of the
number. This decimal point is 12 places
from the end of the number or where
the decimal was originally.
New Decimal Point Original Decimal
Rewrite the number by multiplying it by a
power of ten.
* Drop all zeros and write your number. This
number must be multiplied by a power of 10.
4.600,000,000,000 = 4.6 x 10
* Your exponent will be the number of places
that the decimal point was moved. Since the
decimal point was moved 12 places, the
exponent will be "12".
4.6 x 1012
The term significant figures
refers to the number of
important single digits
(0 through 9) in the coefficient
of an expression in Scientific
1. All nonzero digits are
1.234 g - has 4 significant figures,
1.2 g - has 2 significant figures.
2. Zeroes between nonzero digits
1002 kg - has 4 significant figures,
3.07 mL - has 3 significant figures.
3. Leading zeros to the left of the
first nonzero digits are not
significant; such zeroes merely
indicate the position of the decimal
0.001 mg - has only 1 significant figure
0.012 g - has 2 significant figures.
4. Trailing zeroes that are also to
the right of a decimal point in a
number are significant:
0.0230 ml - has 3 significant figures
0.20 g - has 2 significant figures.
5. When a number ends in zeroes
that are not to the right of a
decimal point, the zeroes are
not necessarily significant:
190 miles may be 2 or 3 significant figures
50,600 calories may be 3, 4, or 5 significant
1. In addition and subtraction, the result is
rounded off to the last common digit
occurring furthest to the right in all
components. Another way to state this
rule is as follows: in addition and
subtraction, the result is rounded off so
that it has the same number of digits as
the measurement having the fewest
decimal places (counting from left to
right). For example,
100 – 3 SF
+ 23.645 – 5 SF
2. In multiplication and division, the
result should be rounded off so as
to have the same number of
significant figures as in the
component with the least number of
significant figures. For example,
12.25 – 4 SF
X 3.0 – 2 SF
36.75 = 37