HOW DO WE CLASSIFY AND USE REAL NUMBERS? 0-2: Real Numbers

Natural Numbers: 1, 2, 3, … Whole Numbers: 0, 1, 2, 3, … Integers: …, -2, -1, 0, 1, 2, … Rational Numbers  Decimals that terminate (have an end)  Decimals that repeat  Fractions where both numerator and denominator are integers Irrational Numbers  Decimals that don’t have a repeating pattern  Square roots that aren’t perfect squares

0-2: Real Numbers Square Root: One of two equal factors of a number  E.g. One square root of 64 (written as ) is 8, because 8 ● 8 = 64. The positive square root is called the principle square root. Another square root of 64 is -8, since -8 ● -8 = 64.  A perfect square is any number where the principle square root is also a rational number.  64 is a perfect square since its principle square roots are 8  2.25 is a perfect square since its principle square root is 1.5

0-2: Real Numbers Name the set or sets of numbers to which each real number belongs 55 / 22 BBecause both 5 and 22 are integers (and because 5/22 = … which is a repeating decimal), this is a rational number BBecause the square root of 81 is 9, this is a natural number, a whole number, an integer, and a rational number BBecause the square root of 56 is …, which does not repeat or terminate, this is an irrational number

Graph each set of numbers on a number line. Then order the numbers from least to greatest. {{ 5 / 3, -4 / 3, 2 / 3, -1 / 3 } 55/3 ≈ --4/3 ≈ 22/3 ≈ --1/3 ≈ {{ -4 / 3, -1 / 3, 2 / 3, 5 / 3 }

Graph each set of numbers on a number line. Then order the numbers from least to greatest. {{, 4.7, 12 / 3, 4 1 / 3 } ssqrt(20) ≈ … 44.7 = 4.7 112/3 = 4 44 1/3 ≈ {{ 12 / 3, 4 1 / 3,, 4.7}

Any repeating decimal can be written as a fraction  Write 0.7 as a fraction  Let N = 0.7  Since one digit repeats, multiply each side by 10 If two digits repeat, multiply each side by 100. If three repeating digits multiply each side by 1000, etc.  10N = 7.7  Subtract N from 10N to eliminate the repeating part  10N = N = 0.7  9N = 7Divide both sides by 9  N = 7 / 9

0-2: Real Numbers You can simplify fractional square roots by simplifying the numerator and denominator separately SSimplify You can estimate roots that are not perfect squares EEstimate to the nearest whole number 99 is a perfect square (3 ● 3) 116 is a perfect square (4 ● 4) BBecause 15 is closer to 16, the best estimate for is 4

Assignment  Page P10  Problems 1 – 35, odds