2-1: REAL NUMBERS AND NUMBER LINES

2-1: Real Numbers and Number Lines  N ATURAL N UMBERS :1, 2, 3, …  W HOLE N UMBERS : 0, 1, 2, 3, …  I NTEGERS :…, -2, -1, 0, 1, 2, …  R ATIONAL N UMBERS : Any number that can be written in the form a/b, which includes any repeating or terminating decimals  I RRATIONAL N UMBERS : Decimals that are nonterminating and do not repeat  R EAL N UMBERS : The collection of all rational and irrational numbers.

2-1: Real Numbers and Number Lines  P OSTULATE 2-1: Each real number corresponds to exactly one point on a number line. Each point on a number line corresponds to exactly one point.  Examples with real numbers  Write a real number with ten digits to the right of the decimal point.  A rational number less than 10 with a 3-digit repeating pattern  An irrational number between -4 and … …

2-1: Real Numbers and Number Lines  C OORDINATE : A point on a number line that corresponds to a number.  O RIGIN : The coordinate 0  P OSTULATE 2-2 (D ISTANCE P OSTULATE ): For any two points on a line and a given unit of measure, there is a unique positive real number called the MEASURE of the distance between the points. AB  Measure 

2-1: Real Numbers and Number Lines  P OSTULATE 2-3 (R ULER P OSTULATE ): The points on a line can be paired with the real numbers so that the measure of the distance between corresponding points is the positive difference of the numbers. AB  --- Measure = a – b -- 

2-1: Real Numbers and Number Lines  Example  The measure of the distance between points R and S is 11 – 3, or 8.  Since the measure from point R to point S is the same as from S to R, you can write RS=8 or SR = 8.

2-1: Real Numbers and Number Lines  Another way to calculate the measure of the distance is by using the absolute value.  A BSOLUTE VALUE : The number of units a number is from zero on a number line.  When using absolute value with subtraction, the order in which the two numbers are subtracted does not matter. RS: | 3 – 11 | = | -8 | = 8 SR: | 11 – 3 | = | 8 | = 8

2-1: Real Numbers and Number Lines  Use the number line above to find the lengths of:  BE  CF  DA  FB

2-1: Real Numbers and Number Lines  Highway markers are a good representation of number lines.  Jamal traveled on the PA Turnpike from Levittown/Bristol to Valley Forge. The Levittown exit is at mile marker 358, and the Valley Forge exit is at mile marker 326. How far did Jamal travel on the Turnpike? | 358 – 326 | = | 32 | Jamal traveled 32 miles

2-1: Real Numbers and Number Lines  Assignment  Worksheet #2-1