3-4 Scientific Notation
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
3-4 Scientific Notation
Warm Up
Multiply.
1. 724  102
2. 837  10
72,400
8,370
3. 632.9  100
63,290
3-4 Scientific Notation
Problem of the Day
A rope ladder is hanging from the back
of a yacht. At 10:00 A.M., the water
reaches the third step on the ladder. If
the water rises the height of 2 steps
every 2 hours, at what step would the
water level be at 5:00 P.M.? Explain.
the third, because the boat will rise
with the water
3-4 Scientific Notation
Learn to write large numbers in scientific
notation.
3-4 Scientific Notation
Vocabulary
scientific notation
3-4 Scientific Notation
Additional Example 1A: Multiplying by Powers
of Ten
Find each product.
5,892  1,000
5,892.000
There are 3 zeros in 1,000.
To multiply, move the decimal
3 places right.
= 5,892,000
Write 3 placeholder zeros.
3-4 Scientific Notation
Additional Example 1B: Multiplying by Powers
of Ten
Find each product.
47.75  10,000
47.7500
There are 4 zeros in 10,000.
To multiply, move the decimal
4 places right.
= 477,500
Write 4 placeholder zeros.
3-4 Scientific Notation
Check It Out: Example 1A
Find each product.
901  1,000
901.000
There are 3 zeros in 1,000.
To multiply, move the decimal
3 places right.
= 901,000
Write 3 placeholder zeros.
3-4 Scientific Notation
Check It Out: Example 1B
Find each product.
15.425  10,000
15.4250
There are 4 zeros in 10,000.
To multiply, move the decimal
4 places right.
= 154,250
Write 4 placeholder zeros.
3-4 Scientific Notation
Scientific notation is a shorthand method that
can be used to write large numbers.
A number written in scientific notation has two
numbers that are multiplied.
4.123  105
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.
3-4 Scientific Notation
Additional Example 2: Writing Numbers in
Standard Notation
Write 6,000,000 in scientific notation.
6,000,000
6,000,000 Move the decimal point 6 places left.
The power of 10 is 6.
6,000,000 = 6  106
3-4 Scientific Notation
Check It Out: Example 2
Write 4,325,000 in scientific notation.
4,325,000 Move the decimal point 6 places left.
The power of 10 is 6.
4,325,000 = 4.325  106
3-4 Scientific Notation
You can write a large number written in
scientific notation in standard form. Look at
the power of 10 and move the decimal
point that number of places to the right.
3-4 Scientific Notation
Additional Example 3: Writing Numbers in
Standard From
Write 6.2174  103 in standard form.
6.2174  103
6.2174
The power of 10 is 3.
Move the decimal point 3 places
right.
6.2174  103 = 6,217.4
3-4 Scientific Notation
Check It Out: Example 3
Write 3.21975  103 in standard form.
3.21975  103
3.21975
The power of 10 is 3.
Move the decimal point 3 places
right.
3.21975  103 = 3,219.75
3-4 Scientific Notation
Additional Example 4
Write the distance to the sun, 93,000,000
miles, in scientific notation.
Move the decimal point left to
93,000,000
form a number that is greater
than or equal to 1 and less than
10.
Multiply that number by a power
93,000,000
of ten.
9.3 
107
The power of 10 is 7, because the
decimal point is moved 7 places
left.
The distance to the sun is 9.3  107.
3-4 Scientific Notation
Check It Out: Example 4
Write the distance 132,500 in scientific
notation.
Move the decimal point left to
132,500
form a number that is greater
than or equal to 1 and less than
10.
Multiply that number by a power
of ten.
132,500
1.325 
105
The power of 10 is 5, because the
decimal point is moved 5 places
left.
The distance is 1.325  105.
3-4 Scientific Notation
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
3-4 Scientific Notation
Lesson Quiz
Write each number in scientific notation.
1. 6,300
6.3  103
2. 70,400,000 7.04  107
Write each number in standard form.
3. 7.241  104 72,410
4. 8.2137  107 82,137,000
5. A Wall Street report indicated that a fast-moving
stock had sold 3,295,000 shares. Write this
number in scientific notation.
3.295  106
3-4 Scientific Notation
Lesson Quiz for Student Response Systems
1. Which of the following represents 9,400
in scientific notation?
A. 9.4  102
B. 9.4  103
C. 94  102
D. 94  103
3-4 Scientific Notation
Lesson Quiz for Student Response Systems
2. Which of the following represents
5,328,000 in scientific notation?
A. 5328  103
B. 532.8  103
C. 53.28  105
D. 5.328  106
3-4 Scientific Notation
Lesson Quiz for Student Response Systems
3. Which of the following represents
1.1132  105 in scientific notation?
A. 11,132,000
B. 1,113,200
C. 111,320
D. 11,132
3-4 Scientific Notation
Lesson Quiz for Student Response Systems
4. Which of the following represents
7.9132  106 in scientific notation?
A. 79,132
B. 791,320
C. 7,913,200
D. 79,132,000
3-4 Scientific Notation
Lesson Quiz for Student Response Systems
5. Jupiter is at a distance of 778,600,000
km from the sun. Identify this number in
scientific notation.
A. 7.786  108
B. 7.786  107
C. 7.786  106
D. 7.786  105