Download Irrational numbers

Making Sense of Rational and
Irrational Numbers
Objectives: Identify number sets.
Write decimals as fractions.
Write fractions as decimals.
The set of real numbers is all numbers that can
be written on a number line. It consists of the set
of rational numbers and the set of irrational
numbers.
Real Numbers
Rational numbers
Integers
Whole
numbers
Irrational numbers
Recall that rational numbers can be written
as the quotient of two integers (a fraction)
or as either terminating or repeating
decimals.
3
4
= 3.8
5
2
= 0.6
3
1.44 = 1.2
Rational Numbers
Natural Numbers - Natural counting numbers.
1, 2, 3, 4 …
Whole Numbers - Natural counting numbers and zero.
0, 1, 2, 3 …
Integers - Whole numbers and their opposites.
… -3, -2, -1, 0, 1, 2, 3 …
Rational Numbers - Integers, fractions, and decimals.
Ex:
-0.76, -6/13, 0.08, 2/3
Irrational numbers can be written only as
decimals that do not terminate or repeat. They
cannot be written as the quotient of two
integers. If a whole number is not a perfect
square, then its square root is an irrational
number. For example, 2 is not a perfect square,
so 2 is irrational.
Caution!
A repeating decimal may not appear to
repeat on a calculator, because
calculators show a finite number of digits.
Identify each root as rational or irrational.
1) 10
2)
irrational
25 rational
6)
62
7) 81
irrational
rational
3) 15 irrational
8)  16 rational
4)  49 rational
9)
5)
50 irrational
99
irrational
10) 121 rational
Decimal to Fraction: A skill
you will need for this unit!
• To change a decimal to a fraction by
dividing the denominator by the numerator
• 5/10= 5 ÷ 10 = 0.5
Complete the table.
Fraction
4
5
3
100
7
20
7
6
10
1
9
8
Decimal
0.8
0.03
0.35
6.7
9.125
Rational and Irrational Numbers
Determine whether the following are rational or irrational.
(a) 0.73
rational
(f)
7
irrational
(b)
2
irrational
(c) 0.666….
rational
(d) 3.142
rational
(e)
12.25
irrational
https://www.youtube.com/watch?v=RPVu3
pYDUFI
RULES FOR ADDING AND MULTIPLYING
RATIONAL AND IRRATIONAL NUMBERS
Rule 1: Rational + Rational = Rational
Example:
Rule 2: Rational x Rational = Rational
Example:
Rule 3: Rational x Irrational = Irrational
Example:
RULES FOR ADDING AND MULTIPLYING
RATIONAL AND IRRATIONAL NUMBERS
Rule 4: Irrational + Rational = Irrational
Example: