Transcript The Real Number System

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Objective
Identify and classify numbers in the real
number system
Vocabulary
Irrational number
A number that cannot be expressed as a/b,
where a and b are integers and b ≠ 0
Vocabulary
Real number
A set of rational and irrational numbers
together
Review
Vocabulary
Rational number
A number that can be expressed as a/b, where
a and b are integers and b ≠ 0
Real Numbers
Rational Numbers
Integers
Whole
Numbers
Negative
Integers
Irrational Numbers
Fractions,
terminating
and
repeating
decimals that
are not
integers
Example 1 Classify Numbers
Example 2 Classify Numbers
Example 3 Classify Numbers
Example 4 Graph Real Numbers
Example 5 Compare Real Numbers
Example 6 Compare Real Numbers
Example 7 Using Real Numbers
Name all sets of numbers to which
belongs.
Write problem
5
Find the value of
Look at the graphic organizer
for numbers
1/7
Real Numbers
Rational Numbers
Irrational Numbers
Integers
5
Whole
Numbers
Negative
Integers
Fractions,
terminating
and
repeating
decimals that
are not
integers
Answer:
Whole number, Integer, Rational Number, Real Number
1/7
Name all sets of numbers to which
Answer: whole number, integer, rational
number, real number
1/7
belongs.
Name all sets of numbers to which
belongs.
Write problem
-3.464101615 . . .
Find the value of
We have a repeating decimal that does NOT end
2/7
Real Numbers
Rational Numbers
Irrational Numbers
-3.464101615 . . .
Integers
Whole
Numbers
Negative
Integers
Fractions,
terminating
and
repeating
decimals that
are not
integers
Answer: Irrational Number, Real Number,
2/7
Name all sets of numbers to which
belongs.
Answer: irrational number, real number
2/7
Name all sets of numbers to which 0.090909… belongs.
0.090909 . . .
Write problem
The decimal ends in a repeating pattern.
3/7
Real Numbers
Rational Numbers
Integers
Whole
Numbers
Negative
Integers
Irrational Numbers
0.090909. . .
Fractions,
terminating
and
repeating
decimals that
are not
integers
Answer:
Repeating Decimal, Rational Number, Real Number,
3/7
Name all sets of numbers to which 0.1010101010…
belongs.
Answer: repeating decimal, rational number, real number
3/7
Estimate
graph
and
and
to the nearest hundredth. Then
on a number line.
Write problem
Evaluate the expressions
2.8284 . . .
2.83
-1.4142 . . .
-1.41
Round to nearest hundredth
4/7
Estimate
graph
and
and
to the nearest hundredth. Then
on a number line.
Draw number line from at least
-2 to 3
Plot solutions on number line
2.8284 . . .
-1.4142 . . .
Label with original expression
2.83
-1.41
Answer:
4/7
Estimate
and
and
to the nearest tenth. Then graph
on a number line.
Answer:
4/7
Replace with <, >, or to make
a true sentence. Round to nearest
hundredth
Write problem using a circle
between the numbers
Convert each to a decimal
3.875
3.88
3.872
>
Answer:
Round to nearest hundredth
Write a comparison
3.87
>
5/7
Replace with <, >, or
a true sentence.
Answer:
to make
>
5/7
Replace with <, >, or
a true sentence.
to make
Write problem using a circle
between the numbers
Convert each to a decimal
3.222 . . .
<
3.2249
Must compare the
thousandths position
Write a comparison
Answer:
<
6/7
Replace with <, >, or
a true sentence.
Answer:
to make
>
6/7
BASEBALL The time in seconds that it takes an
object to fall d feet is
How many seconds
would it take for a baseball that is hit 250 feet straight
up in the air to fall from its highest point to the
ground?
Write the expression
Replace d with 250
0.25 (15.81)
3.95
Answer:
Follow order of operations
P
E
MD
AS
Find the square root
Multiply
3.95 seconds
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*
BASEBALL The time in seconds that it takes an
object to fall d feet is
How many seconds
would it take for a baseball that is hit 450 feet straight
up in the air to fall from its highest point to the
ground?
Answer: 5.31 seconds
7/7
Assignment
Lesson 3:3
The Real Number
System
14 - 48 All