Rational & Irrational Numbers

1. Rational & Irrational Numbers

2. Rational Numbers The real number system consists of rational and irrational numbers. Rational numbers can be expressed in fractional form, , where a (the numerator) and b (the denominator) are both integers and b = 0. The decimal form of the number either terminates or repeats. Counting numbers, whole numbers, integers, and non-integers are all rational numbers. a b

3. Counting numbers are the natural numbers. {1, 2, 3, 4, 5, 6, …} Whole numbers consist of the counting numbers and zero. {0, 1, 2, 3, 4, 5, …} Integers consist of the counting numbers, their opposites, and zero. {…, -3, -2, -1, 0, 1, 2, 3, …}

4. Non-integers consist of fractions that can be written as terminating or repeating decimals. • A terminating decimal comes to a complete stop. • A repeating decimal continues the same digit or block of digits forever. 1 3 2 5.25 0.6 -9.261 7 3

5. Irrational Numbers Irrational numbers are numbers that cannot be written as a ratio of two integers. Irrational numbers are non-repeating and non-terminating decimals because the decimal form of the number never ends and never repeats. The most common irrational number is pi (п). The value of п is 3.141592654…

6. Example 1 Tell whether each real number is rational or irrational. -23.75 rational decimal terminates 4.750918362… irrational decimal does not terminate 5 9 √15 irrational decimal form does not terminate rational number is in fraction form

7. HOMEWORK Complete worksheet “Rational & Irrational Numbers”