Scientific Notation
Math
Lesson 2.5
Ms. Baggett
Vocabulary:
Notation –
A number written in scientific notation
has the form c x 10n where c is
greater than or equal to 1 and less
than 10 and n is a whole number.
 Scientific
Using Scientific Notation:
A number is written in scientific notation if is
has the form c x 10n where c is greater
than or equal to 1 and less than 10 and n
is a whole number.
Standard Form
Scientific Notation
2,860,000
2.86 x 106
Example 1: Writing Numbers in
Scientific Notation
Budget The budget to support the national
parks in the United States was
$64,500,000 in scientific notation,
use powers of 10.
Standard Form
64,500,000
Scientific Notation
6.45 x 107
Answer: The budget for national parks in the
United States was $6.45 x 107 in 1998.
Remember…Powers of Ten!
100 = 1
101 = 10
102 = 100
103 = 1,000
104 = 10,000
105 = 100,000
106 = 1,000,000
Writing Numbers in Standard Form
Write the number in standard form.
a. 3 x 105
Solution:
Scientific Notation
a. 3 x 105
b. 6.702 x 109
b. 6.702 x 109
Standard Form
300,000
6,702,000,000
Your turn now.
Write the number in scientific notation.
1. 27,500,000
2.
10,200,000,000
3.
3,600,000
Let’s look at the answers on the board together.
Your turn now.
Write the number in standard form.
4. 6.37 x 104
5.
2.09 x 107
6.
1 x 101
Let’s look at the answers on the board
together.
Example 3: Comparing Numbers in
Scientific Notation
Population The population of Alaska was
about 6.35 x 105 in 2001. The population
of Nebraska was about 1.71 x 106 in 2001,
which state had the greater population?
Solution
To compare numbers written in scientific
notation, first compare the exponents, then
compare the decimal parts.
Example 3 Continued:
Alaska: 6.35 x 105
Exponent is 5.
Nebraska: 1.71 x 106
Exponent is 6.
Because 5 < 6, 6.35 x 105 < 1.71 x 106
Answer: Nebraska had the greater
population.
Example 3 Continued:
Check Write the numbers in standard form
and compare.
6.35 x 105
=
635,000
1.71 x 106
=
1,710,000
So, 6.35 x 105 < 1.71 x 106.
Your turn now.
Copy and complete the statement using <,
>, or =.
7.
3.4 x 1030 ___ 2.05 x 1032
8.
2.59 x 1015 ___ 2.06 x 1015
Let’s look at these on the board together.