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The Real Number SystemReal Numbers
Rational Numbers
... -1.5, -1, -0.5, 0, 0.5, 1, 1.5, …
Integers
... -3, -2, -1, 0, 1, 2, 3, …
Whole Numbers
0, 1, 2, 3, 4, 5, 6, …
Natural Numbers 1, 2, 3, 4, 5, 6, …
... 2, 1.816, 0, 1, 2, ... Irrational Numbers
2, 3, , 11...
The Real Number Line
| | | | | | | | | | |
-5 -4 -3 -2 -1 0 1 2 3 4 5
Integers
-5 -4 -3 -2 -1 0 1 2 3 4 5
NaturalNumbers
-5 -4 -3 -2 -1 0 1 2 3 4 5
WholeNumbers
| | | | | | | | | | |
-5 -4 -3 -2 -1 0 1 2 3 4 5 -4.5 -2.5 0.33 1.7 2.9 4.1
RationalNumbers
2 5
Irrational Numbers
Remember that Irrational Numbers
do not have an exact point on the number
line.
Square RootsA number is a Perfect Square if it is the product of two Identical Factors. 6 6 36
10 10 100
2 2 4
5 5 25
7 7 49These are all perfect squares because they are the product of two identical factors.
Common Perfect SquaresHere is a list of the first 20 perfect
squares.
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
I should probably try to remember those.
Evaluating Square Roots
Evaluate the following radicals
16 25 9 81
400 225 169 529
4 5 3 9
A number is a Perfect Square if it is the product of two Identical Factors.
20 15 13 23
More Evaluating Radicals
121 5.291681
2.8912.25
11 2.349
1.73.5
These are all Rational Numbers
15 20 90 80
3.87 4.47 9.49 8.94
These are all Irrational Numbers
More Irrational Roots
Irrational Roots will always fall between two consecutive
integers.Between what two consecutive integers is each square root?
35 130 217
Between5 and 6
Between-12 and -11
Between14 and 15
Asi De Facil That was easy
between
144 2& 1 1
between
25 & 36
between
196 & 225
Homework
Page 20: 10 – 22 & 28 - 36Even Numbers Only
Expressing a Decimal as a Rational Number
Write the fraction as the given number over the place value. Reduce the resulting fraction if possible.
0.3 0.225 0.2375 0.0325
310
2251,000
940
2,37510,000
1980
32510,000
13400
A rational number is any number that can be written in the form
ab
Expressing Rational Numbers as a Decimal
A rational number is any number that can be written in the form
Common Fractions Decimal FractionsWritten with a
numerator and a denominator.
12
34
116
To express as a decimal, perform the
division.
.5
.75
.0625
The numerator is written after the decimal point and the denominator is
indicated by the place value of the last digit.
0.5
0.75
0.0625
1510 2
7510
30 4
62510,0 100
16
These are all terminating decimals.
ab
Repeating Decimals
The same number, or pattern of numbers, repeats.
13
0.3333333333 0.3
23
0.6666666667 0.6
49
0.4444444444 0.4
211
0.1818181818 0.18
433
0.1212121212 0.12
833
0.2424242424 0.24
That was easy
Symbols of InequalitySymbol
Example
Written in Words
9 2 9 is greater than 2
2 9 2 is less than 9
9 2 9 is greater than or equal to 2
2 9 2 is less than or equal to 9
2 9 2 is not equal to 9
Comparing Real NumbersCompare the following numbers with an inequality symbol.17,
14
3
Write each as
a decimal
4.1231, 4.3
Compare the
decimals4.1231 4.3
Write the answer with the original
numbers
117 4
3
25
3, 29
5.6 5., 3852
5.6 5.3852
25 29
3
43
, 2
1.3 1., 4142
1.3 1.4142
42
3
711
, 0.63
,0.63 0.63
0.63 0.63
70.63
11
Ordering Numbers from Least to Greatest
Order the numbers in each group from least to greatest.
3.2 3.002 3.023.002 3.02 3.2
2.021 2.21 2.0021 2.21 2.021 2.0021
5 3 25 5 5
12 4 3
5.416 5.75 5.6
1 72 5 2.4
2 4
0.5 2 2.2361 1.75 2.4
2 1.75 0.5 2.2361 2.4
5 2 35 5 5
12 3 4
7 12 5 2.4
4 2
5.416 5.6 5.75
Homework
Page 20: 38 - 50Even Numbers
Only
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