IRRATIONAL NUMBERS The mystery and intrigue abounds!

CCSS.Math.Content.8.NS.A.1 CCSS.Math.Content.8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. THAT IS NOT SAYING TOO MUCH ABOUT THE IRRATIONALS! CCSS.Math.Content.8.NS.A.2 CCSS.Math.Content.8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π 2 ). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

No repeating Pattern For example, is irrational. THIS INDICATES THE RICHNESS OF THESE NUMBERS WHICH ARE UNCOUNTABLE

RATIONAL APPROXIMATIONS?

ARITHMETIC?

THE MOST FAMOUS IRRATIONAL NUMBER π≈ Currently 12.1 x digits are known

DIGITS OF π

2800 DIGITS OF π REPEAT DIGITS ARE CONNECTED

11400 DIGITS OF π REPEAT DIGITS ARE CONNECTED

FROM THE WEBSITE VISUAL CINNAMON. EACH DIGIT IS A COLOR AND A DIRECTION.

200 million searchable digits of PI

Star Trek and π

What’s a Continued Fraction?

THERE ARE IRRATIONALS w,z so that