Download Scientific Notation

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Scientific Notation
Goal: Read and write numbers using scientific notation.
Vocabulary
Scientific notation:
A number written in scientific notation has the
form c 10 n where c is greater than or equal
to 1 and less than 10 and n is a whole number.
Using Scientific Notation
A number is written in scientific notation if it has the form c 10n
where c is greater than or equal to 1 and less than 10 and n is
a whole number .
Standard form
Product form
2,860,000
2.86 1,000,000
EXAMPLE
Powers of ten:
101 = 10
102 = 100
103 = 1000
104 = 10,000
105 = 100,000
106 = 1,000,000
1
Scientific notation
2.86 10
6
Writing Numbers in Scientific Notation
Budget The budget to support the national parks in the United States
was $64,500,000 in 1998. To write 64,500,000 in scientific notation,
use powers of 10.
Standard form
64,500,000
Product form
Scientific notation
6.45 10,000,000
6.45 10
7
Answer: The budget for national parks in the United States was
$ 6.45 10 7 in 1998.
Lesson 2.5
Scientific Notation
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EXAMPLE
2
Writing Numbers in Standard Form
Write the number in standard form.
You read
3 x 105 as
"three times
ten to the fifth
power."
a. 3 105
b. 6.702 109
Solution
Scientific
notation
Product
form
a. 3 105
3 100,000
b. 6.702 109
Guided Practice
1. 27,500,000
2.75 107
Standard
form
300,000
6.702 1,000,000,000
6,702,000,000
Write the number in scientific notation.
2. 10,200,000,000
1.02 1010
3. 3,600,000
3.6 10 6
Write the number in standard form.
4. 6.37 104
63,700
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Chapter 2
Notetaking Guide
5. 2.09 107
20,900,000
6. 1 101
10
EXAMPLE
3
Comparing Numbers in Scientific Notation
Population The population of Alaska was about 6.35 105 in 2001.
The population of Nebraska was about 1.71 106 in 2001. Which state
had the greater population?
Solution
To compare numbers written in scientific notation, first compare the
exponents . If the exponents are equal , then compare the
decimal parts .
Alaska: 6.35 105
Exponent is 5 .
Nebraska: 1.71 106
Exponent is 6 .
Because 5 < 6, 6.35 105 < 1.71 106.
Answer:
Nebraska had the greater population.
✓ Check Write the numbers in standard form and compare.
6.35 105 635,000
1.71 106 1,710,000
So, 6.35 105 < 1.71 106.
Guided Practice
Copy and complete the statement using <, >, or ⴝ.
7. 3.4 1030 ____
? 2.05 1032
8. 2.59 1015 ____
? 2.06 1015
<
>
Lesson 2.5
Scientific Notation
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