THE REAL NUMBERS AND ABSOLUTE VALUE SECTION 2.1

Real Numbers Rationals Irrationals Integers Whole Natural

rational Real numbers – the set of both ____________ and _______________ numbers. irrational ends Irrational numbers – Decimal that never ________ and never ____________. repeats Rational numbers – Any number that can be written as a decimal that either ___________ or ___________________. ends repeats Integers - ( ___________ , _________, ___________) negatives ( _______ , ___________) zero positives zero postives ( _______ , ____________) Whole numbers - Natural numbers - ( _____________ ) postives

positives negatives zero -4 -3 -2 -1 1 2 3 4

Less than greater than Equal to Less than or equal to Symbols used for ordering numbers: Less than Less than or equal to greater than greater than or equal to Equal to

Example 1: Insert an ordering symbol to make each statement true.

Try these…. B. A. D. C.

On the number line, two numbers that lie on opposite sides of 0 and are the same _______________ from 0 are called ______________. distance opposites -6 The opposite of 6 is _____. 3 The opposite of -3 is _____.

The opposite of a positive is always __________. When finding the opposite of any number, use the opposite symbol. opposite opposite The opposite of a positive is always __________. The opposite of a negative is always __________. The opposite of zero is always _______. negative positive zero

Example 2: Evaluate each expression: B. C.

Try these… D. E. F.

means the absolute value of The ________________ of a real number is the distance it is from ________ on a number line. absolute value zero The symbol means the absolute value of Example 3: Simplify: B. C. A. D.

Try these… E. F. G.