Download Rational numbers

1-5 Roots and Real Numbers
Warm Up
Simplify each expression.
2. 112 121
1. 62 36
3. (–9)(–9) 81
25
36
4.
Write each fraction as a decimal.
5. 2 0.4
6. 5
0.5
5
9
7. 5 3 5.375
8
Holt McDougal Algebra 1
8. –1
5
6
–1.83
1-5 Roots and Real Numbers
Objectives
Classify numbers within the real number
system.
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Real numbers can be classified according to their
characteristics.
Natural numbers are the counting
numbers: 1, 2, 3, …
Whole numbers are the natural numbers
and zero: 0, 1, 2, 3, …
Integers are the whole numbers and their
opposites: –3, –2, –1, 0, 1, 2, 3, …
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Rational numbers are numbers that can be
expressed in the form , where a and b are both
integers and b ≠ 0. When expressed as a
decimal, a rational number is either a terminating
decimal or a repeating decimal.
• A terminating decimal has a finite number of
digits after the decimal point (for example, 1.25,
2.75, and 4.0).
• A repeating decimal has a block of one or more
digits after the decimal point that repeat
continuously (where all digits are not zeros).
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Irrational numbers are all numbers that are not
rational. They cannot be expressed in the form
where a and b are both integers and b ≠ 0. They
are neither terminating decimals nor repeating
decimals. For example:
0.10100100010000100000…
After the decimal point, this number contains 1
followed by one 0, and then 1 followed by two
0’s, and then 1 followed by three 0’s, and so
on.
This decimal neither terminates nor repeats, so it is
an irrational number.
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
If a whole number is not a perfect square, then its
square root is irrational. For example, 2 is not a
perfect square and
is irrational.
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
The real numbers are made up of all rational
and irrational numbers.
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Reading Math
Note the symbols for the sets of numbers.
R: real numbers
Q: rational numbers
Z: integers
W: whole numbers
N: natural numbers
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Let’s Try together…
Write all classifications that apply to each
real number.
A. –32
32
1
–32 = –32.0
–32 = –
–32 can be written in the form
.
–32 can be written as a terminating
decimal.
rational number, integer, terminating decimal
B.
irrational
Holt McDougal Algebra 1
14 is not a perfect square, so
irrational.
is
1-5 Roots and Real Numbers
Let’s Try together…
Write all classifications that apply to each real
number.
a. 7
7 4 can be written in the form
9
.
can be written as a repeating
decimal.
rational number, repeating decimal
b. –12
–12 can be written in the form .
–12 can be written as a
terminating decimal.
rational number, terminating decimal, integer
67  9 = 7.444… = 7.4
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Let’s Try together…
Write all classifications that apply to each real
number.
irrational
10 is not a perfect square, so
is irrational.
100 is a perfect square, so
is rational.
10 can be written in the form
and as a terminating decimal.
natural, rational, terminating decimal, whole, integer
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Find each square root.
1.
3
2.
3.
5
4.
1
5. The area of a square piece of cloth is 68 in2.
Estimate to the nearest tenth the side length
of the cloth.  8.2 in.
Write all classifications that apply to each
real number.
6. –3.89 rational, repeating
decimal
Holt McDougal Algebra 1
7.
irrational
1-5 Roots and Real Numbers
Try each problem WITHOUT looking at your notes
Write all possible classifications of each number
1. -53
integer
Natural, whole, integer,
2.
rational, terminating decimal
3.
2/3
Holt McDougal Algebra 1
Rational, repeating decimal
1-5 Roots and Real Numbers
4.
5.
1/2
√12
6. –3.89
7.
Holt McDougal Algebra 1
Rational, terminating decimal
irrational
Rational, repeating decimal
irrational
1-5 Roots and Real Numbers
Always, Sometimes, Never…
1.A negative number is an integer
2.A repeating decimal is irrational
3.Mixed numbers are rational
4.A terminating decimal is a rational number
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Always, Sometimes, Never…
1.A negative number is an integer
SOMETIMES -√2
2. A repeating decimal is irrational NEVER
3. Mixed numbers are rational ALWAYS
4. A terminating decimal is a rational number
ALWAYS
Holt McDougal Algebra 1
1-5 Roots and Real Numbers
Pre-Requisite Packet – Front page…
Holt McDougal Algebra 1