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Scientific Notation
Section 7-2
Goals
Goal
• To write numbers in
scientific notation and
standard form.
• To compare and order
numbers using scientific
notation.
Rubric
Level 1 – Know the goals.
Level 2 – Fully understand the
goals.
Level 3 – Use the goals to
solve simple problems.
Level 4 – Use the goals to
solve more advanced problems.
Level 5 – Adapts and applies
the goals to different and more
complex problems.
Vocabulary
• Scientific Notation
Powers of 10
The table shows relationships between several powers
of 10.
• Each time you divide by 10, the exponent in the power
decreases by 1 and the decimal point in the value moves one
place to the left.
• Each time you multiply by 10, the exponent in the power
increases by 1 and the decimal point in the value moves one
place to the right.
Powers of 10
• You can find the product of a number and a power
of 10 by moving the decimal point of the number.
– If the exponent is positive, move the decimal point to
the right.
– If the exponent is negative, move the decimal point to
the left.
• You may need to write zeros to the right or left of
the number in order to move the decimal point.
Example: Multiplying by
Powers of 10
Multiply.
A. 14  104
14.0 0 0 0
Since the exponent is a positive 4, move
the decimal point 4 places to the right.
140,000
B. 3.6  10-5
0 0 0 0 3.6
0.000036
Since the exponent is a negative 5, move
the decimal point 5 places to the left.
Your Turn:
Multiply.
A. 2.5  105
2.5 0 0 0 0
Since the exponent is a positive 5, move the
decimal point 5 places to the right.
250,000
B. 10.2  10-3
0 10.2
0.0102
Since the exponent is a negative 3, move the
decimal point 3 places to the left.
Definition
• Scientific Notation - is a way to express numbers
that are very large or very small.
– Powers of 10 are used when writing numbers in
scientific notation.
– Numbers written in scientific notation are expressed as
2 factors.
• One factor is a number greater than or equal to 1.
• The other factor is a power of 10.
– Example:
• 1.43 ⨯ 1012
• 5.8 ⨯ 10-9
Scientific Notation
The first part is a number that is greater than or
equal to 1 and less than 10.
The second part is a power of 10.
Why Use Scientific
Notation?
• For very large and very small numbers,
these numbers can be converted into
scientific notation to express them in a more
concise form.
• Numbers expressed in scientific notation
can be used in a computation with far
greater ease.
Example: Recognizing
Scientific Notation
Is the number written in scientific notation?
Explain.
1. 53 ⨯ 104
No, 53 is not less than 10
2. 3.42 ⨯ 10-7
Yes
3. 0.35 ⨯ 102
No, 0.35 is not greater than or
equal to 1
4. 9.6 ⨯ 100
No, 100 is not in power of 10 form
Your Turn:
Is the number written in scientific notation?
Explain.
1. 8.15 ⨯ 10-6
Yes
2. 12.9 ⨯ 108
No, 12.9 is greater than 10
3. 1.003 ⨯ 107
Yes
4. 0.0045 ⨯
No, 0.0045 is not greater than
or equal to 1
10-32
Procedure: Writing Numbers
in Scientific Notation
1. Place the decimal point so that there is one nonzero digit to the left of the decimal point.
2. Count the number of decimal places the decimal
point has “moved” from the original number.
This will be the exponent on the 10.
3. If the original number was less than 1, then the
exponent is negative. If the original number was
greater than 1, then the exponent is positive.
Example: Writing Numbers in
Scientific Notation
Write the number in scientific notation.
A. 0.00709
7.09  10-3
Think: The decimal needs to move 3 places to
get a number between 1 and 10.
Think: The number is less than 1, so the
exponent will be negative.
So 0.00709 written in scientific notation is 7.09  10–3.
Example: Writing Numbers in
Scientific Notation
Write the number in scientific notation.
B. 23,000,000,000
2.3  1010
Think: The decimal needs to move 10
places to get a number between 1 and
10.
Think: The number is greater than 1,
so the exponent will be positive.
So 23,000,000,000 written in scientific notation is 2.3  1010.
Your Turn:
Write the number in scientific notation.
Think: The decimal needs to move 4
places to get a number between 1 and 10.
A. 0.000811
-4
8.11  10
Think: The number is less than 1, so the
exponent will be negative.
So 0.000811 written in scientific notation is 8.11  10–4.
Your Turn:
Write the number in scientific notation.
B. 480,000,000
4.8  108
Think: The decimal needs to move 8
places to get a number between 1 and
10.
Think: The number is greater than 1,
so the exponent will be positive.
So 480,000,000 written in scientific notation is 4.8  108.
Reading Math
Standard form refers to the usual way that
numbers are written—not in scientific
notation.
Procedure: Writing Numbers
in Standard Form
1. Simply move the decimal point to the right
for positive exponent 10.
2. Move the decimal point to the left for
negative exponent 10.
(Use zeros to fill in places.)
Example: Writing a
Number in Standard Form
Write the number in standard form.
A. 1.35  105
1.35  10
5
1.35000
135,000
Think: Move the decimal right 5 places.
Example: Writing a
Number in Standard Form
Write the number in standard form.
B. 2.7  10–3
2.7  10–3
0002.7
0.0027
Think: Move the decimal left 3 places.
Your Turn:
Write the number in standard form.
A. 2.87  109
2.87  10
9
2.870000000
2,870,000,000
Think: Move the decimal right 9 places.
Your Turn:
Write the number in standard form.
B. 1.9  10–5
1.9  10
–5
000001.9
0.000019
Think: Move the decimal left 5 places.
Example: Comparing Numbers
in Scientific Notation
A certain cell has a diameter of approximately 4.11  10-5 meters. A
second cell has a diameter of 1.5  10-5 meters. Which cell has a
greater diameter?
4.11  10-5
1.5  10-5
Compare the exponents.
4.11 > 1.5
Compare the values between 1 and
10.
Notice that 4.11  10-5 > 1.5  10-5.
The first cell has a greater diameter.
Your Turn:
A star has a diameter of approximately
5.11  103 kilometers. A second star has a diameter of 5  104
kilometers. Which star has a greater diameter?
5.11  103
5  104
Compare the exponents.
Notice that 3 < 4. So 5.11  103 < 5  104
The second star has a greater diameter.
Example: Ordering Numbers
in Scientific Notation
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
Step 2 Order the numbers that have the same power of 10
Your Turn:
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
2  10-12, 4  10-3, 5.2  10-3, 3  1014, 4.5  1014,
4.5  1030
Step 2 Order the numbers that have the same power of 10
Joke Time
• Did you hear about the red ship and the blue ship that
collided?
• Both crews were marooned!
• What did one shark say to the other while eating a
clownfish?
• This tastes funny!
• What did the cobbler say when a cat wandered into his
shop?
• Shoe!
Assignment
• 7-2 Exercises Pg. 450 - 452: #12 – 48 even