IRRATIONAL NUMBERS The mystery and intrigue abounds CCSS

IRRATIONAL NUMBERS The mystery and intrigue abounds!

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. 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. , π2). 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. THAT IS NOT SAYING TOO MUCH ABOUT THE IRRATIONALS!

No repeating Pattern • For example, 0. 123456789101112131415161718192021. . . is irrational. THIS INDICATES THE RICHNESS OF THESE NUMBERS WHICH ARE UNCOUNTABLE

RATIONAL APPROXIMATIONS?

ARITHMETIC? •

THE MOST FAMOUS IRRATIONAL NUMBER π≈3. 14159265358 Currently 12 12. 1 x 10 digits are known

3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 700 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.

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 •