Download When dealing with very large or very small numbers

When dealing with very large or very
small numbers, keeping track of place
value can be difficult. For this reason,
numbers such as these are often
expressed in scientific notation.
Scientific Notation
A number is expressed in scientific notation
when it is written as a product of a factor
and a power of 10. The factor must be
greater than or equal to 1 and less than or
equal to 10.
A number in scientific notation is written as
a x 10n, where 1≤ a < 10 and n is an integer.
The following examples show one way
of expressing a number that is written
in scientific notation in its decimal or
standard notation. Look for a
relationship between the power of 10
and the position of the decimal point in
the standard notation of the number.
6.59 x 104 = 6.59 x 10,000
= 65,900
The decimal place moved 4 places to
the right.
4.81 x 10-6 = 4.81 x 1
106
= 4.81 x 0.000001
=0.00000481
The decimal point moved 6 places to
the left.
These examples suggest the following
rule for expressing a number written in
standard notation in scientific notation.
Scientific to Standard Notation
Use these steps to express a number
of the form a x 10n in standard notation.
• Determine whether n > 0 or n < 0.
• If n > 0, move the decimal point in a to the
right n places.
• If n < 0, move the decimal point in a to the
left n places.
• Add zeros, decimal point, and/or commas
as needed to indicate place value.
Standard to Scientific Notation
• Move the decimal point so that it is to the right of
the first nonzero digit. The result is a decimal
number a.
• Observe the number of places n and the
direction in which you moved the decimal point.
• If the decimal point moved to the left, write as a
x 10n.
• If the decimal point moved to the right, write as
a x 10-n.
You will often see large numbers in the
media written using a combination of a
number and a word, such as 3.2
million. To write this number in
standard notation, rewrite the word
million as 106. The exponent 6
indicates that the decimal point should
be moved 6 places to the right.
3.2 million = 3,200,000
Products and Quotients with Scientific
Notation
You can use scientific notation to
simplify computation with very large
and/or very small numbers.