Transcript 1-3 Real Numbers and the Number Line

1-3
Real Numbers and
the Number Line
The radical symbol
square root
indicates a nonnegative
Problem 1: Simplifying Square Root
Expressions
What is the simplified form of
each expression
81
Problem 1: Simplifying Square Root
Expressions
What is the simplified form of
each expression
9
16
Problem 1: Simplifying Square Root
Expressions
What is the simplified form of
each expression
64
Problem 1: Simplifying Square Root
Expressions
What is the simplified form of
each expression
1
36
The square of an integer is called a
perfect square. 49 is a perfect square
2
because 7 = 49 is a perfect square.
When a radicand is not a perfect
square, you can estimate the square
root.
Problem 2: Estimating
a Square Root
Lobster eyes are made of tiny square
regions. Under a microscope, the
surface of the eye looks like graph
paper. A scientist measures the area of
one of the squares to be 386 square
microns. What is the approximate side
of the square to the nearest micron?
Problem 2: Estimating
a Square Root
What is the value of 34 to the
nearest integer
Problem 4:
Comparing Real Numbers
Inequality: a mathematical sentence that
compares the values of two expressions
using an inequality symbol.
< LESS THAN
> GREATER THAN
 LESS THAN OR EQUAL TO
 GREATER THAN OR EQUAL TO
What is an inequality that compares
1
17 𝑎𝑛𝑑 4
3
What is an inequality that compares
129 𝑎𝑛𝑑 11.52
Problem 5:
Graphing and Ordering Real Numbers
2
4, 0.4, − ,
3
What is the order of
2,
𝑎𝑛𝑑 − 1.5 from least to greatest.
Then order on a number line.
Problem 5:
Graphing and Ordering Real Numbers
What is the order of 3.5, −2.1, 9,
7
− , 𝑎𝑛𝑑 5 from least to greatest.
2
Then order on a number line.
Problem 3:
Classifying Real
Number
𝑎
,
𝑏
Rational Number: In the form
where a and b are integers and 𝑏 ≠
0. In decimal form they are
terminating decimal such as 5.45 or a
repeating decimal such as 0.416666…
which you can write as 0.416
Natural numbers: also called counting numbers
and are the ones you count with {1, 2, 3, …}
Whole Numbers: include the natural numbers,
but also includes zero
{0, 1, 2, 3, …}
Integers: The whole numbers, plus their
respective negative numbers {…, -3, -2, -1, 0, 1,
2, 3, …}
Irrational numbers: cannot be written
as a fraction. In decimal form, irrational
numbers do not terminate or repeat.
(some square roots are rational and
some are irrational)
(if a whole number is not a perfect
square, its square is irrational ex: 3 =
1.73205080 …)
Rational numbers and irrational
numbers form the set of Real
numbers
To which subsets of the real number
system does each number belong?
• 15
• −1.4583
• 57
•
3
10