Transcript 9-5 Scientific_Notation

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
Over Lesson 9–4
Write 2–3 using a positive exponent.
A. (–3)2
B. 23
C.
D.
Over Lesson 9–4
Write a–1 using a positive exponent.
A. a
B. –a
C.
D.
Over Lesson 9–4
Write (–5)–4 using a positive exponent.
A.
B.
C. 54
D. (–5)4
Over Lesson 9–4
A. 45
B. 4–5
C. (–4)–5
D.
Over Lesson 9–4
A. 49–0
B. 7–2
C. 4–9
D.
Over Lesson 9–4
Evaluate z–3 if z = 5.
A. 125
B. –125
C.
D.
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.
• standard form
• scientific notation
Express Numbers in Standard Form
A. Express 3 × 105 in standard form.
3 × 105 = 3 × 100,000
= 300,000
Answer: 300,000
105 = 100,000
Move the decimal
point 5 places to the
right.
Express Numbers in Standard Form
B. Express 4.395 × 104 in standard form.
4.395 × 104 = 4.395 × 10,000
= 43950
Answer: 43,950
104 = 10,000
Move the decimal
point 4 places to the
right.
Express Numbers in Standard Form
C. Express 6.79 × 10–6 in standard form.
6.79 × 10–6 = 6.79 × 0.000001
= 0.00000679
Answer: 0.00000679
10–6 = 0.000001
Move the decimal point
6 places to the left.
A. Express 5 × 104 in standard form.
A. 5,000
B. 50,000
C. 500,000
D. 5,000,000
B. Express 2.614 × 106 in standard form.
A. 2,614,000
B. 261,400
C. 0.000002614
D. 0.002614
C. Express 8.03 × 10–4 in standard form.
A. 80,300
B. 8.030
C. 0.000803
D. 0.0803
Express Numbers in Scientific Notation
A. Express 800,000 in scientific notation.
800,000 = 8.0 × 100,000
= 8.0 × 105
Answer: 8.0 × 105
The decimal point moves
5 places.
The exponent is positive.
Express Numbers in Scientific Notation
B. Express 64,000 in scientific notation.
64,000 = 6.4 × 10,000
= 6.4 × 104
Answer: 6.4 × 104
The decimal point moves
4 places.
The exponent is positive.
Express Numbers in Scientific Notation
C. Express 0.0119 in scientific notation.
0.0119 = 1.19 × 0.01
= 1.19 × 10–2
Answer: 1.19 × 10–2
The decimal point moves
2 places.
The exponent is negative.
A. Express 65,000 in scientific notation.
A. 6.5 × 105
B. 6.5 × 10–4
C. 6.5 × 104
D. 65 × 103
B. Express 95,000,000 in scientific notation.
A. 9.5 × 106
B. 9.5 × 107
C. 95 × 106
D. 95 × 107
C. Express 0.00042 in scientific notation.
A. 42 × 10–5
B. 4.2 × 10–4
C. 4.2 × 104
D. 4.2 × 10–3
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.
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 
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. 1.75 × 106 m
B. 1.75 × 109 m
C. 1.75 × 1012 m
D. 1.75 × 1015 m
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.
Order Numbers in Scientific Notation
Step 2
Order the numbers with the same exponent
by comparing the factors.
5.1
>
Uranus
5.1 × 104 >
4.9
Neptune
4.9 × 104
Answer: So, the order is Saturn, Uranus, and Neptune.
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