Download Lesson 5.5: Rational Numbers and Decimals

8/27/15
1. Please complete the
“conclusion” questions on the
back of your scavenger hunt.
2. Share with a neighbor.
3. Let’s share out.
Making Sense of Rational and
Irrational Numbers
Essential Question: How are
rational and irrational
numbers simplified?
Biologists classify animals based on
shared characteristics. The horned
lizard is an animal, a reptile, a lizard, and
a gecko!
Animal
Reptile
Lizard
Gecko
Numbers can also be
classified!
The set of real numbers is all numbers that can
be written on a number line.
It consists of 2 subsets –
rational numbers and irrational numbers.
Real Numbers
Rational numbers
Integers
Whole
numbers
Irrational numbers
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
Name all the sets of numbers to which the given
number belongs. Circle the most specific set.
1)  5
Integer , Rational
2
2)
3
Rational
3) 16
Naturals , Whole, Integer , Rational
4) 0
Whole , Integer , Rational
5)  0.7 Rational
Venn Diagram
Real Numbers
Rational
6.7
5

9
0.8
Integer
11
Whole
Natural
1, 2, 3...
5
0
3
2
7
Remember…
Rational numbers can be written as a
fraction
or…
as either a terminating or repeating
decimal.
4
35
= 3.8
2 = 0.6
3
1.44 = 1.2
Classify the Following:
•
23
– Irrational
• -0.33333…
– Rational (equals -⅓)
Classify the Following:
• 0.818811888111…
– Irrational (no end, no repetition)
• 1⅔
– Rational (can be 5/3 )
• 100
– Rational (equals 10 or 10/1 )
Rational v. Irrational – How alike?
• Subsets of Real numbers
• Can be negative
• Can be non-terminating
(never end)
Rational v. Irrational – How different?
• Rational:
– CAN be a fraction
– HAS a perfect
square root
– Can be
terminating or
repeating decimals
• Irrational:
– CANNOT be a
fraction
– Has NO perfect
square root
– Can only be nonterminating, nonrepeating decimals
Irrational numbers can be written only as
decimals that do not terminate or repeat.
They cannot be written as a fraction.
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 limited 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 need for this unit!
• To change a decimal to a fraction, take the
place value and simplify!
• 0.5 means “5 tenths,” so start with 5/10
• Now simplify 5/10 to ½
• So… 0.5 = ½
Converting Fractions and Decimals
Fraction
Decimal
3
8
means 3  8
0 37 5
8 3.000
24
60
56
40
40
0
0.375
To change a fraction to a decimal, take
the top divided by the bottom, or
numerator divided by the denominator.
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
Repeating Decimals
Fraction
1
3
means 1  3
0 3 33...
3 1.000
9
10
9
10
9
1
Decimal
0.3
0.33
Every rational number (fraction) either terminates
OR repeats when written as a decimal.
Repeating Decimals
Fraction
5
11
means 5  11
0 4 54 54 ...
11 5.00000
44
60
55
50
44
60
55
50
44
6
Decimal
0.454
0.454
0.45
Repeating Decimals
Fraction
5
6
means 5  6
0 8 33...
6 5.000
48
20
18
20
18
2
Decimal
0.83
0.833
0.83
Rational Numbers
o CAN be made into a fraction a/b,
where b ≠ 0.
o A repeating OR terminating
decimal.
o 2/3  0.6
o 25  5
o 0.798798798…
Irrational Numbers
• CANNOT be made into a fraction
a/ , where b ≠ 0.
b
• A non-repeating AND nonterminating decimal number.
oπ
o 5
o 0.313311333111…