3-4 - Mr. C. Street
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Transcript 3-4 - Mr. C. Street
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