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1.3 – Real Numbers and the Number Line
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I.SQUARES and SQUARE ROOTS: The term square root comes from the AREAS of squares and their sides. Because 9 = 3 2, we say that 3 is a SQUARE ROOT of 9
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The symbol for theis called the RADICAL. The expression under the radical is the RADICAND. Together they form the SQUARE ROOT. In general, if A = s 2, then s is called a square root of A
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Squares and Square Roots you should know: Examples: Simplify the following: 1) 2) 3) 4) x123456789101112131415 x2x2 149162536496481100121144169196225
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The square of an integer is a PERFECT SQUARE. To estimate a perfect square, find the two nearest perfect squares and determine which is closer. Estimate the square root. Round to the nearest integer. 1) 2) 3) 4)
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II. Sets of numbers A SET is a well defined collection of objects. Each object is called an ELEMENT of the set. A SUBSET of a set consists of elements from the given set. You can list the elements of a set between BRACES: { }
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Frequently Used Sets of Numbers Natural Numbers: 1, 2, 3, 4,… Whole Numbers: 0, 1, 2, 3, 4,… Integers: …, -2, -1, 0, 1, 2, … Rational Numbers: … Irrational Numbers: …
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Rational Numbers include any terminating or repeating decimal numerals. Rational numbers include any number that can be written in the form where a and b are both integers where
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Irrational Numbers include infinite non- repeating decimals. Real numbers include all rational and irrational numbers.
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Natural Whole Integers Rational Irrational Real
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The square of an integer is a PERFECT SQUARE. To estimate a perfect square, find the two nearest perfect squares and determine which is closer. Name the subset(s) of the real numbers to which each number belongs. 1) 2) 3) 4)
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Comparing Real Numbers: An INEQUALITY is a mathematical sentence the compares the values of two expressions using an inequality symbol. Less thanGreater than Less than or equal to Greater than or equal to
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Example: Compare the following with an inequality symbol 1) Rewrite as decimal: 2) Compare the decimals: 3) Write using an inequality:
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Example: Compare the following using a number line: 1) Rewrite as decimals: 2) Plot on a number line: 3) Write using an inequality:
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Homework : TUESDAY: Section 1.3pages 23-25 #’s 1-8, 10, 14, 16, 17, 20, 22, 23, 26, 29, 33, 37, 41 WEDNESDAY: #’s 13, 19, 25, 29, 34, 40, 42, 46, 48, 60, 65, 66, 67, 68
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