Scientific Notation
Objective Learn how to write very large and
small numbers in scientific notation and to compare and order
numbers written in scientific notation.
Scientific notation is a useful topic for many applications.
It also provides a great opportunity to reinforce your
understanding of place value in terms of powers of ten.
Very Large and Very Small Numbers
Let's see some very large and very small numbers. A few
examples are listed.
• The mass of the planet Pluto is roughly
12,900,000,000,000,000,000,000 kilograms.
• The number of molecules in a cubic centimeter of oxygen
at standard temperature and pressure is about
602,000,000,000,000,000,000,000.
• A typical cell membrane is about 0.00000001 meter
thick.
• A large virus has a diameter of roughly 0.0000001
meter.
Each of the numbers shown above contains many zeros. Thus, it
may be difficult to read and compare them. However, there is a
notation that can be used to express all of the zeros in a
simple, easy to read form. Consider the following examples.
Example 1
7,000,000,000 (seven
billion) 
= 7 Ã— (one billion) 

= 7 Ã— 10^{ 9} One billion is
equal to 10^{ 9}. 
Notice how few symbols are required to write 7 Ã— 10^{ 9}
compared to 7,000,000.
Example 2
13,000,000 (thirteen
million) 
= 13 Ã— (one million) 

= 13 Ã— 10^{ 6} One billion is
equal to 10^{ 6}. 

= 1.3 10^{ 7} 1.3 is one tenth of 13. 
Example 3
0.0000056 (fiftysix tenmillionths)
= 5 Ã— (one millionth) + 6 Ã— (one
tenmillionth) 




1,000,000 = 10^{ 6 }and
10,000,000 = 10^{ 7} 
= 5 Ã— 10^{ 6} + 6 Ã—10^{ 7}

Laws of Negative Exponents 
= (5 + 6 Ã—10^{ 1} ) Ã— 10^{
6} 
Factor 10^{ 6 }. 
= 5.6 Ã— 10^{ 6} 

Key Idea
Every nonzero number can be written as a number greater than
or equal to one and less than ten times a power of ten.
Definition of Scientific Notation
A number that is written as a number between 1 and 10 times a
power of ten is said to be written in scientific notation.
All of the following numbers are written in scientific
notation.
1.2 Ã—10^{ 6}
2.4 Ã—10^{ 5}
5.8 Ã—10^{ 18}
The following numbers are not written in scientific notation
because the number in front of the multiplication sign is not
between 1 and 10.
12.5 Ã—10^{ 12}
0.15 Ã—10^{ 11}
235 Ã—10^{ 13}
