# Real Numbers (subsets of real numbers and ordering real numbers)

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Real Numbers (subsets of real numbers and ordering real numbers)

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Definitions to know Natural (or counting) numbers: N= {1,2,3…}
Whole numbers: W={0,1,2,3…} Integers: {…-3,-2,-1,0,1,2,3…} Rational numbers: Q={all numbers that can be expressed in the form m/n, where m and n are integers and n is not zero}. The decimal form of a rational number is either a terminating or repeating decimal. Irrational number: I={all nonterminating, nonrepeating decimals}. Any number that is not a perfect square has an irrational square root. Real numbers: R={all rationals and irrationals}

Shortcut Real Numbers- (R) Irrational Numbers- (I)
Rational Numbers- (Q) Integer- (Z) Whole Numbers- (W) Natural Numbers- (N)

Real Numbers Real numbers can be divided into two basic groups: Irrational numbers and Rational numbers. Rational Numbers can further be divided into 3 groups: integers, whole numbers, and natural numbers.

Rational Numbers Rational numbers are all numbers that can be expressed in the form m/n, where m and n are integers and n is not zero}. The decimal form of a rational number is either a terminating or repeating decimal. A natural number is also always : a whole number, integer, rational number, and real number, etc. Although a natural number is always an integer; an integer is not always a natural number, etc. Example: 2, 8/2, 15, 83= real/rational/ integer /whole /natural -2,-8/2,-15,-83= real/rational/ integer Rational numbers (Q) Integers (Z) Whole numbers (W) Natural Numbers (N)

Irrational Numbers Irrational numbers are all nonterminating, nonrepeating decimals. Any number that is not a perfect square has an irrational square root. Examples: …. ….. 17

Examples of Real Number’s Subsets
3/4= real/ rational 0= real/rational/integer/whole ….= real/irrational 1= real/rational/integer/whole/natural = real/irrational 1/3= real/ rational 91,215,225,201,544= real/rational/integer/whole/natural

Practice 1(subsets of real numbers)
Which of the following numbers is irrational? A -1/2 B 3.63 C 121 D 6/55

Practice 2 (subsets of real numbers)
 36 is what kind of number? A Real/ Irrational B Real/rational/integer/ whole/natural C Real/rational/integer/whole D Real/rational

Practice 3 (subsets of real numbers)
Which of the following is a rational number? A 3 B C 1/5 D 25/115

Practice 4 (subsets of real numbers)
-6 is what kind of number? A Real/rational/integer B Real/irrational C Real/rational D Real/rational/integer/ whole

Ordering Real Numbers Real numbers are ordered from least to greatest.
Example: 1, -4, 49, -16/2, 19/5 ordered from least to greatest would be: -16/2 (-8), -4, 1, 49 (7), 19/5(3.8)

Practice 5 (ordering real numbers)
Order the following numbers from smallest to largest: -8, 14/3, 10, 5 A -8, 14/3, 10, 5 B -8, 5, 14/3, 10 C -8, 10, 5, 14/3 D -8, 14/3, 5, 10

Practice 6 (ordering real numbers)
Order the following numbers from least to greatest: 144, -47, 19/6, -13 A -47, -13, 19/6, 144 B -47, -13, 144, 19/6 C -13, -47, 144, 19/6 D -47, 144, 19/6, -13

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