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Main Idea and New Vocabulary
NGSSS
Key Concept: Irrational Numbers
Example 1:Classify Numbers
Example 2:Classify Numbers
Example 3:Classify Numbers
Example 4:Compare Real Numbers
Example 5: Compare Real Numbers
Example 6: Compare Real Numbers
Example 7: Order Real Numbers
Example 8: Real-World Example
Five-Minute Check
• Compare mathematical expressions involving real numbers.
• irrational number
• real number
MA.8.A.6.2 Make reasonable approximations of square roots and mathematical expressions that include square roots, and use them to estimate solutions to problems and to compare mathematical expressions involving real numbers and radical expressions.
Classify Numbers
Name all sets of numbers to which the real number 0.090909… belongs.
Answer: The decimal ends in a repeating
pattern.
It is a rational number because it is
equivalent to .
A. whole
B. rational
C. whole, integer, rational
D. irrational
Name all sets of numbers to which the real number 0.454545… belongs.
Classify Numbers
Name all sets of numbers to which the real number belongs.
Answer: Since = 5, it is a whole number, an integer, and a rational number.
A. whole
B. whole, integer
C. whole, integer, rational
D. irrational
Name all sets of numbers to which the real number belongs.
Classify Numbers
Name all sets of numbers to which the real number belongs.
Answer: –3.464101615… Since the decimal does not terminate or repeat,
it is an irrational number.
A. whole
B. integer, rational
C. whole, integer, rational
D. irrational
Name all sets of numbers to which the real number belongs.
Compare Real Numbers
Write each number as a decimal.
Replace with <, >, or = to make a true statement.
Compare Real Numbers
Since 3.872983346… is less than 3.875, .
Answer:
A. <
B. >
C. =
Replace with <, >, or = to make 4 a
true statement.
Compare Real Numbers
Write as a decimal.
≈ 3.224903099…
= 3.222222222…
Replace with <, >, or = to make a true statement.
Compare Real Numbers
Since 3.222222222… is less than 3.224903099…,
Answer:
Compare Real Numbers
Write each number as a decimal.
12.3% = 0.123
= 0.1
Replace with <, >, or = to make 12.3% ● a true statement.
Compare Real Numbers
Answer: 12.3% >
Since 0.123 is greater than 0.1, 12.3% > .
A. <
B. >
C. =
Replace with <, >, or = to make 90% a true statement.
Write each number as a decimal. Then order the decimals.
3 = 3.00
Order Real Numbers
Order from least to greatest.
Verify your answer by graphing on a number line.
Order Real Numbers
Answer: From least to greatest, the order is
3, , , and 4 .
BEACH VOLLEYBALL The time in seconds that it
takes an object to fall d feet is About how
many seconds would it take for a volleyball
thrown 32 feet up in the air to fall from its highest
point to the sand?
Use a calculator to approximate the time it would take for a volleyball to fall to the sand.
Answer: It would take a volleyball thrown 32 feet up in the air about 1.4 seconds to fall to the sand.
Replace d with 32.
≈ 1.4 s Use a calculator.
A. about 70 s
B. about 9.7 s
C. about 2.5 s
D. about 1.1 s
PHYSICAL SCIENCE The time in seconds that it
takes an object to fall d feet is About how
many seconds longer would it take for a ball
dropped from 100 feet to fall to the ground than a
ball dropped from 30 feet?
A. whole
B. integer
C. whole, integer
D. whole, integer, rational
Name all sets of numbers to which the real number 286 belongs.
A. integer
B. integer, rational
C. whole, integer, rational
D. irrational
Name all sets of numbers to which the real number belongs.
A. sometimes
B. always
C. never
Are irrational numbers sometimes, always, or never rational numbers?
A. real
B. fractions
C. rational
D. negative integers
To which set does NOT belong?
