Rational and Irrational Numbers
Rational and Irrational Number Imagine you are standing at the origin (0,0) of a perfectly square, infinite forest.Trees are planted at every single whole-number coordinate intersection—for example, at (1,1), (2,1), (5,3), and so on.Every tree trunk is infinitely thin (like a literal mathematical point). 1. Looking at Rational Numbers (Visible Trees)If you turn your head and look out into the forest at a specific angle, your line of sight represents a slope.If you look along a slope that is a rational number (like 0.5, which is 1/2, your line of sight will eventually hit a tree (the tree at coordinate x=2, y=1).In fact, because the forest is infinite, you will hit an infinite number of trees perfectly lined up behind it (4,2), (6,3), etc. 2. Looking at Irrational Numbers (The Hidden Pathways)What if you look along a slope that is an irrational number, like square root 2(approximately 1.4142...) or π = approx 3.14...? Fractions used in everyday math—suc...