1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Multiply.
 102
 10
 100
72,400
8,370
63,290

3. 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

4. Learn to write large numbers in scientific notation.

5. Vocabulary
scientific notation

6. Additional Example 1A: Multiplying by Powers of Ten
Find each product.
5,892  1,000
There are 3 zeros in 1,000. 5,
To multiply, move the decimal 3 places right.
= 5,892,000
Write 3 placeholder zeros.

7. Additional Example 1B: Multiplying by Powers of Ten
Find each product.
47.75  10,000
There are 4 zeros in 10,000.
To multiply, move the decimal 4 places right.
= 477,500
Write 4 placeholder zeros.

8. Check It Out: Example 1A
Find each product.
901  1,000
There are 3 zeros in 1,000.
To multiply, move the decimal 3 places right.
= 901,000
Write 3 placeholder zeros.

9. Check It Out: Example 1B
Find each product.
 10,000
There are 4 zeros in 10,000.
To multiply, move the decimal 4 places right.
= 154,250
Write 4 placeholder zeros.

10. 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.

11. Additional Example 2: Writing Numbers in Standard Notation
Write 6,000,000 in scientific notation.
6,000,000
Move the decimal point 6 places left.
The power of 10 is 6.
6,000,000
6,000,000 = 6  106

12. Check It Out: Example 2
Write 4,325,000 in scientific notation.
Move the decimal point 6 places left.
The power of 10 is 6.
4,325,000
4,325,000 =  106

13. 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.

14. Additional Example 3: Writing Numbers in Standard From
Write  103 in standard form.
 103
The power of 10 is 3.
6.2174
Move the decimal point 3 places right.
 103 = 6,217.4

15. Check It Out: Example 3
Write  103 in standard form.
 103
The power of 10 is 3.
Move the decimal point 3 places right.
 103 = 3,219.75

16. Additional Example 4
Write the distance to the sun, 93,000,000 miles, in scientific notation.
93,000,000
Move the decimal point left to form a number that is greater than or equal to 1 and less than 10.
Multiply that number by a power of ten.
93,000,000
The power of 10 is 7, because the decimal point is moved 7 places left.
9.3  107
The distance to the sun is 9.3  107.

17. Check It Out: Example 4
Write the distance 132,500 in scientific notation.
132,500
Move the decimal point left to 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
The power of 10 is 5, because the decimal point is moved 5 places left.
1.325  105
The distance is  105.

18. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

19. Lesson Quiz
Write each number in scientific notation.
1. 6,300
2. 70,400,000
Write each number in standard form.
 104
 107
5. A Wall Street report indicated that a fast-moving stock had sold 3,295,000 shares. Write this number in scientific notation.
6.3  103
7.04  107
72,410
82,137,000
3.295  106

20. 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

21. Lesson Quiz for Student Response Systems
2. Which of the following represents 5,328,000 in scientific notation?
A  103
B  103
C  105
D  106

22. Lesson Quiz for Student Response Systems
3. Which of the following represents  105 in scientific notation?
A. 11,132,000
B. 1,113,200
C. 111,320
D. 11,132

23. Lesson Quiz for Student Response Systems
4. Which of the following represents  106 in scientific notation?
A. 79,132
B. 791,320
C. 7,913,200
D. 79,132,000

24. 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  108
B  107
C  106
D  105