The document discusses the classification of numbers in the real number system. It describes rational numbers as numbers that can be written as fractions with integer numerators and non-zero denominators, including integers. Rational numbers can be expressed with terminating or repeating decimals. Irrational numbers cannot be expressed as fractions and their decimal representations do not terminate or repeat. The real number system consists of both rational numbers, such as integers and numbers with terminating or repeating decimals, and irrational numbers like π.

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1. Math Essentials - Unit 1: Classification of the Real Number System
2. Math Objective – The student will be able to;
 Describe and classify types of numbers that make up the Real Number System
3. Real Numbers – The Real Number System consist of both Rational and Irrational
Numbers. These numbers can be pictured as points on a real n umber line.
4. Rational Numbers consist of:
a. Natural Numbers or the set of counting numbers. For example, the set that
contain numbers 1, 2, 3, 4, 5, 6, and so forth.
b. Whole numbers or the set of natural numbers (or counting numbers) that include
the number ‘0.’ For example the set that contains the numbers 0, 1, 2, 3, 4, 5, 6,
and so forth
c. Integers or the set of whole numbers and their opposites. For example, the set
that contains 0, 1, 2, 3, 4, 5, and so forth as well as their opposites -1, -2, -3, -4, -
5, and so forth
5. Rational numbers, by definition, are any numbers that can be expressed in the form a
over b, where a and b are integers and b does not equal 0. For example, integer can be
written with a denominator of ‘1’ such as -3/1, -2/1, -1/1, 0/1, 1/1, 2/1, 3/1, and so forth.
Rational numbers can also be expressed by using terminating or repeating decimals.
6. Terminating decimals are decimals that contain a finite number of digits. For example,
0.75, 2.5, -10.25, -0.5 and so forth. Note, the above examples correspond to the fractions
¾, 2 ½, -10 ¼, - ½. Repeating decimals are decimals that contain an infinite number of
digits. For example, 0.333 with 3 repeating, -2.666 with 6 repeating, 0.8181 with 81
repeating. Note, the above examples correspond to the fractions 1/3, -2 2/3, 9/11.
7. An Irrational number, by definition, is a number that cannot be written as a fraction and
the decimal equivalent does not terminate nor repeat. For example, π (Pi) is an irrational
number that has the value 3.14159265358979324626433832795 and so forth. The
decimal number continues forever with no repeating pattern. Radicals that cannot
simplify to a rational number are irrational. For example, square root of 2 has the value
1.414213562373095 and so forth. Another example is the cube root of 7 which has the
value 1.912931182772389 and so forth.

2. 8. In summary, the real number system can represented as 2 huge subsets of numbers,
rational and irrational. A subset of rational numbers is integers and a subset of integers is
whole numbers. A subset of whole numbers is natural numbers.
9.