1. Splash Screen

2. Five-Minute Check (over Lesson 9–4) Then/Now New Vocabulary
Key Concept: Scientific Notation
Example 1: Express Numbers in Standard Form
Example 2: Express Numbers in Scientific Notation
Example 3: Real-World Example: Solve Problems Using Scientific Notation
Example 4: Real-World Example: Order Numbers in Scientific Notation
Lesson Menu

3. Write 2–3 using a positive exponent.
B. 23 C. D.
5-Minute Check 1

4. Write a–1 using a positive exponent.
A. a
B. –a C. D.
5-Minute Check 2

5. Write (–5)–4 using a positive exponent.B.
C. 54
D. (–5)4
5-Minute Check 3

6. A. 45
B. 4–5
C. (–4)–5 D.
5-Minute Check 4

7. A. 49–0
B. 7–2
C. 4–9 D.
5-Minute Check 5

8. Evaluate z–3 if z = 5.
A. 125
B. –125 C. D.
5-Minute Check 6

9. You have already compared and ordered integers. (Lesson 2–1)
Express numbers in standard form and in scientific notation.
Compare and order numbers written in scientific notation.
Then/Now

10. standard form
scientific notation
Vocabulary

11. Concept

12. A. Express 3 × 105 in standard form.
Express Numbers in Standard Form
A. Express 3 × 105 in standard form.
3 × 105 = 3 × 100, = 100,000
= 300,000 Move the decimal point 5 places to the right.
Answer: 300,000
Example 1

13. B. Express 4.395 × 104 in standard form.
Express Numbers in Standard Form
B. Express × 104 in standard form.
4.395 × 104 = × 10, = 10,000
= Move the decimal point 4 places to the right.
Answer: 43,950
Example 1 B

14. C. Express 6.79 × 10–6 in standard form.
Express Numbers in Standard Form
C. Express 6.79 × 10–6 in standard form.
6.79 × 10–6 = 6.79 × –6 =
= Move the decimal point 6 places to the left.
Answer:
Example 1 C

15. A. Express 5 × 104 in standard form.
B. 50,000
C. 500,000
D. 5,000,000
Example 1 CYP A

16. B. Express 2.614 × 106 in standard form.C D
Example 1 CYP B

17. C. Express 8.03 × 10–4 in standard form.B C D
Example 1 CYP C

18. A. Express 800,000 in scientific notation.
Express Numbers in Scientific Notation
A. Express 800,000 in scientific notation.
800,000 = 8.0 × 100,000 The decimal point moves 5 places.
= 8.0 × 105 The exponent is positive.
Answer: 8.0 × 105
Example 2 A

19. B. Express 64,000 in scientific notation.
Express Numbers in Scientific Notation
B. Express 64,000 in scientific notation.
64,000 = 6.4 × 10,000 The decimal point moves 4 places.
= 6.4 × 104 The exponent is positive.
Answer: 6.4 × 104
Example 2

20. C. Express 0.0119 in scientific notation.
Express Numbers in Scientific Notation
C. Express in scientific notation.
= 1.19 × 0.01 The decimal point moves 2 places.
= 1.19 × 10–2 The exponent is negative.
Answer: × 10–2
Example 2 C

21. A. Express 65,000 in scientific notation.
B. 6.5 × 10–4
C. 6.5 × 104
D. 65 × 103
Example 2 CYP A

22. B. Express 95,000,000 in scientific notation.
D. 95 × 107
Example 2 CYP B

23. C. Express 0.00042 in scientific notation.
B. 4.2 × 10–4
C. 4.2 × 104
D. 4.2 × 10–3
Example 2 CYP C

24. Solve Problems Using Scientific Notation
DIMES A dime is 1.35 × 10–3 meters thick. What would the height of a stack of one million dimes be in scientific notation?
Understand You know that a dime is 1.35 × 10–3 meters thick and that there are 1 million dimes in the stack. You need to know how thick the stack is.
Plan Write 1 million in scientific notation. Multiply the thickness of a dime by the number of dimes in the stack to find the total thickness of the stack.
Example 3

25. thickness of = thickness of 1 dime × stack number in stack
Solve Problems Using Scientific Notation
Solve 1 million = 1.0 × 106
thickness of = thickness of 1 dime × stack number in stack
= (1.35 × 10–3 m) × (1.0 × 106)
= 1.35 × 10–3 + 6 m
= 1.35 × 103 m
Answer: So, the height of the stack is 1.35 × 103 m.
Check Check using mental math.
(1.35 × 10–3)(1 × 106) = (1.35 × 1.0)(10–3 × 106)
= 1.35 × 103 
Example 3

26. A quarter is 1. 75 × 10–3 meters thick
A quarter is 1.75 × 10–3 meters thick. What would be the height of a stack of one billion quarters in scientific notation?
A × 106 m
B × 109 m
C × 1012 m
D × 1015 m
Example 3

27. Step 1 Order the numbers according to their exponents.
Order Numbers in Scientific Notation
SPACE The diameters of Neptune, Saturn, and Uranus are 4.9 × 104 km, 1.2 × 105 km, and 5.1 × 104 km, respectively. Order the planets from greatest to least diameter.
Step 1 Order the numbers according to their exponents.
Saturn has the greatest exponent so it is the largest.
Example 4

28. Answer: So, the order is Saturn, Uranus, and Neptune.
Order Numbers in Scientific Notation
Step 2 Order the numbers with the same exponent by comparing the factors.
5.1 > 4.9
Uranus Neptune
5.1 × 104 > 4.9 × 104
Answer: So, the order is Saturn, Uranus, and Neptune.
Example 4

29. A. Mercury, Earth, Jupiter B. Mercury, Jupiter, Earth
The diameters of Earth, Jupiter, and Mercury are 1.55 × 108 km, 7.79 × 108 km, and 5.80 × 107 km, respectively. Order the diameters from smallest to largest diameter.
A. Mercury, Earth, Jupiter
B. Mercury, Jupiter, Earth
C. Earth, Jupiter, Mercury
D. Earth, Mercury, Jupiter
Example 4

30. End of the Lesson