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1-3: Exploring Real Numbers Essential Question: What is a rational number? How can you express an integer as a rational number?

1-3: Exploring Real Numbers  Natural Numbers1, 2, 3, …  Whole Numbers0, 1, 2, 3, …  Integers…-2, -1, 0, 1, 2, …  There are also numbers that are not integers, like 0.37 and ½. These are called rational numbers. A rational number is any number you can write as a fraction where a and b are integers, and b ≠ 0  What does that mean??

1-3: Exploring Real Numbers  Rational numbers are:  Decimals that terminate (end)  Decimals that repeat (e.g. 8.222…, which can be written as 8.2)  Fractions where both numerator and denominator are integers  Irrational numbers are:  Decimal that don’t have a repeating pattern  Square roots that aren’t perfect squares (use a calculator to test)

1-3: Exploring Real Numbers  Name the set(s) of numbers to which each number belongs NumberNatural Number Whole Number IntegerRational Number Irrational Number - 17 / 31 √ 23 √√√√ 0 √√√ 4.581 √  √

1-3: Exploring Real Numbers  Y OUR T URN : Name the set(s) of numbers to which each number belongs NumberNatural Number Whole Number IntegerRational Number Irrational Number 7 - 20 / 4 -7.34 1.010110111… √√√√ √ √√ √ √

1-3: Exploring Real Numbers  An inequality is a mathematical sentence that compares the value of two expressions using an inequality symbol, such as  When you compare two real numbers, only one of these can be true: 1. a < ba is less than b 2. a = ba is equal to b 3. a > ba is greater than b  There are two good ways to order two numbers 1. Put them on a number line. The number that appears first is less than the one that appears second. 2. Subtract the two numbers. If the result is positive, the first number is greater than the second (and vice versa)

1-3: Exploring Real Numbers WWrite - 3 / 8, - 1 / 2, and - 5 / 12 in order from least to greatest CConvert fractions to decimals (it’ll make things easier) -- 3 / 8 = -0.375 -- 1 / 2 = -0.5 -- 5 / 12 = -0.41666… OOrder the decimals from least to greatest --0.5 < -0.41666… < -0.375 -- 1 / 2 < - 5 / 12 < - 3 / 8 YYour Turn WWrite 1 / 12, - 2 / 3, and - 5 / 8 in order from least to greatest -- 2 / 3 < - 5 / 8 < 1 / 12

 Two numbers that are the same distance from zero on a number line but lie in opposite directions are opposites.  The absolute value of a number is its distance from 0 on a number line. Because distance is always positive, both -3 and 3 have an absolute value of 3. You write “the absolute value of -3” as |-3|  Example 5: Find each absolute value  |12| = 12  |- 2 / 3 | = 2 / 3  |0| = 0

1-3: Exploring Real Numbers  Y OUR T URN : Find each absolute value  |5|  |-4|  |-3.7|  | 5 / 7 | 5 4 3.7 5/75/7

1-3: Exploring Real Numbers  Assignment  Worksheet 1-3  Problems 1 – 33, odd  Skip problems 9 & 11

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