The Real Numbers
Mathematics, Grade 8
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• Numbers used in everyday life are real numbers. • Real numbers are used to measure quantities such as temperature, speed of a car or volume of liquid in a cup. • Real numbers are classified as either rational or irrational. Properties of Real Numbers Rational Numbers Irrational Numbers Property Property Addition Addition Multiplication Multiplication Associative Commutative Identity Inverse Distributive a + b = b + a a + 0 = a a • 1 = a a • b = b • a a + (b + c) = (a + b) + c a + (-a) = 0 (-a) + a = 0 a • (b • c) = (a • b) • c (b + c) a = ba + ca or If a = 0, then a • = 1 or a 1 a 1 • a = 1 b a • The Density Property is an important property of real numbers. It states that between any two real numbers there’s another real number. • Rational numbers can be written as a ratio of two integers, such as , where b is not zero. • Rational numbers can also be written as a decimal that is either a terminating or repeating decimal. • Real numbers that are not rational are irrational. • Irrational numbers cannot be written as ratios. • The decimal form of irrational numbers neither repeats nor terminates. • any number that has a position on a number line Ratio Form Decimal Form 0.27272727.... or (0.2727) 0.375 3.141592654....... 2.718281828....... 1.4142135....... 4.0 8 3 11 3 16 2 e Integers -3, -2, -1, 0, 1, 2, 3 Whole numbers 0, 1, 2, 3... Natural numbers 1, 2, 3, 4, 5... Real Numbers Examples: Examples: and a (b + c) = ab + ac Irrational Numbers Rational Numbers • non-terminating, non-repeating decimals • any square root that is not a perfect root © Copyright NewPath Learning. All Rights Reserved. 93-4803 www.newpathlearning.com The Real Numbers
• Numbers used in everyday life are . • Real numbers are used . • Real numbers are classified as either rational or irrational . Properties of Real Numbers Rational Numbers Irrational Numbers Property Property Addition Addition Multiplication Multiplication Associative Commutative Identity Inverse Distributive • The Density Property is an important property of real numbers. It states that . • Rational numbers can be written as • Rational numbers can also be written as • Real numbers that are not rational are irrational. • Irrational numbers cannot be written as ratios. • The decimal form of irrational numbers neither repeats nor terminates. • Real Numbers Key Vocabulary Terms • associative property • commutative property • decimal • distributive property • identity property • integers • inverse property • irrational numbers • natural numbers • non-terminating decimal • ratio • rational numbers • real numbers • square root • terminating decimal • whole number . . . . . . Irrational Numbers Rational Numbers • • © Copyright NewPath Learning. All Rights Reserved. 93-4803 www.newpathlearning.com The Real Numbers \|xiBAHBDy01690ozX
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