Irrational Numbers

Irrational Number √2 ∏ (Pi or 3.14) A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written as a decimal, an irrational number would have an infinite number of digits to the right of the decimal point without repetition. ∏ (Pi or 3.14) √2

Decimal Numbers Terminating Rational Repeating Rational ¼ = .25 Repeating Rational 100/3 = 33.3333 = 33.3 19/27 = 0.703703703 = 0.703 Non-repeating Irrational ∏=3.14159265358979323846264338327950288419716939937510582097494459230781640628 620899862803482534211706798214808651328230664709384460955058223172535940812848 111745028410270193852110555964462294895493038196442881097566593344612847564823 378678316527120190914564856692346034861045432664821339360726024914127372458700 660631558817488152092096282925409171536436789259036001133053054882046652138414 695194151160943305727036575959195309218611738193261179310511854807446237996274 956735188575272489122793818301194912983367336244065664308602139494639522473719 070217986094370277053921717629317675238467481846766940513200056812714526356082 778577134275778960917363717872146844090122495343014654958537105079227968925892 354201995611212902196086403441815981362977477130996051870721134999999837297804 995105973173281609631859502445945534690830264252230825334468503526193118817101 000313783875288658753320838142061717766914730359825349042875546873115956286388 235378759375195778185778053217122680661300192787661119590921642019…

Rational or Irrational? 3.25 √5 √16 100/3 13.33 Repeating Decimal 10∏

Approximate √36 = 6 √49 = 7 7 6 5 4 3 2 1 √38

Compare √36 = 6 √49 = 7 7 6 5 4 3 2 1 √38 √38 > 6 √38 < 14/2

Approximate Irrational Numbers to 2 digit decimal 12 = 1 22 = 4 32 = 9 42 = 16 52 = 25 62 = 36 72 = 49 82 = 64 92 = 81 102 = 100 √1 = 1 √4 = 2 √9 = 3 √16 = 4 √25 = 5 √36 = 6 √49 = 7 √64 = 8 √81 = 9 √100 = 10 √20 4 < √20 < 5 4.52 = 20.25 4.252 = 18.06 4.452 = 19.80 4.482 = 20.07 4.472 = 19.98 4.472 = 19.98

Approximate Irrational Numbers to 2 digit decimal √1 = 1 √4 = 2 √9 = 3 √16 = 4 √25 = 5 √36 = 6 √49 = 7 √64 = 8 √81 = 9 √100 = 10 √52 7 < √52 < 8 7.52 = 56.25 7.252 = 52.56 7.202 = 51.84 7.222 = 52.13 7.212 = 51.98 7.212 = 51.98

Approximate Irrational Numbers to 2 digit decimal √1 = 1 √4 = 2 √9 = 3 √16 = 4 √25 = 5 √36 = 6 √49 = 7 √64 = 8 √81 = 9 √100 = 10 √6 2 < √6 < 3 2.52 = 6.25 2.252 = 5.06 2.402 = 5.76 2.452 = 6.00

Irrational Review Rational Irrational Fraction Terminating decimal Repeating decimal Perfect square Irrational Decimal that never repeats (Pi aka π) Not a perfect square