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Chapter 2-7
The Real Number System
The set of rational numbers and the set of irrational number together form the set of
REAL NUMBERS.
Natural Numbers = {1, 2, 3, …}
Whole Numbers = {0, 1, 2, 3, …}
Integers = {…, -2, -1, 0, 1, 2, …}
Rational Numbers: a/b where b ≠ 0. The decimal form of a rational number is a
terminating or repeating decimal.
Irrational numbers: the decimal form of a irrational number is a non-terminating, nonrepeating decimal.
Completeness Property for Points on the Number Line
Distance between two points. Subtract lesser from the greater.
Examples:
Find distance (d) between -0.25 and 1/3
-1/4 and 1/3
-3/12 and 4/12
d = 4/12 - - 3/12
d = 4/12 + 3/12
d = 7/12
Find the distance (d) between п and -√8 (round to nearest hundredth)
d = 3.14 - - 2.83
d = 3.14 + 2.83
d = 5.97
Find the distance (d) between √5 and √9
√5 = 2.24
√9 = 3
d = 3 – 2.24
d = 0.76
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Density Property of Real Numbers: between any two real numbers, there are other real
numbers.
Find the midpoint between each pair of numbers.
To find the “Midpoint” add the two numbers than find their average (÷2)
Example:
5.256 and 1 ½
Midpoint = 5.235 + 1.5
2
= 6.735/2
= 3.3675 (round to nearest thousandths if needed) = 3.368
Midpoint of 2 3/10 and 2.41
= 2.3 + 2.41
2
= 4.71 ÷ 2
= 2.355
Label each of the numbers as: natural numbers, whole numbers, integers, rational
numbers, irrational numbers.
Reminder:
Natural Numbers = {1, 2, 3, …}
Whole Numbers = {0, 1, 2, 3, …}
Integers = {…, -2, -1, 0, 1, 2, …}
Rational Numbers: a/b where b ≠ 0. The decimal form of a rational number is a
terminating or repeating decimal.
Irrational numbers: the decimal form of a irrational number is a non-terminating, nonrepeating decimal.
Example:
п is irrational
-√144 is -12 which is: integer, rational number
√90 is irrational
9.456456456….: rational
- 6 3/5: rational
117/13 is 9: rational, integer, whole, natural.