Irrational Numbers Irrational Number A number that cannot

Irrational Numbers

Irrational Number • 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 • 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 √ 16 100/3 13. 33 Repeating Decimal 10∏

Approximate √ 38 7 √ 49 = 7 6 √ 36 = 6 5 4 3 2 1 0

Compare √ 38 7 √ 49 = 7 6 √ 36 = 6 5 4 3 2 1 0 √ 38 > 6 √ 38 < 14/2

Approximate Irrational Numbers to 2 digit decimal √ 20 4 < √ 20 < 5 4. 52 = 20. 25 4. 252 = 18. 06 4. 452 = 19. 80 4. 482 = 20. 07 4. 472 = 19. 98 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

Approximate Irrational Numbers to 2 digit decimal √ 52 7 < √ 52 < 8 7. 52 = 56. 25 7. 252 = 52. 56 7. 202 = 51. 84 7. 222 = 52. 13 7. 212 = 51. 98 √ 1 = 1 √ 4 = 2 √ 9 = 3 √ 16 = 4 √ 25 = 5 √ 36 = 6 √ 49 = 7 √ 64 = 8 √ 81 = 9 √ 100 = 10

Approximate Irrational Numbers to 2 digit decimal √ 6 2 < √ 6 < 3 2. 52 = 6. 25 2. 252 = 5. 06 2. 402 = 5. 76 2. 452 = 6. 00 √ 1 = 1 √ 4 = 2 √ 9 = 3 √ 16 = 4 √ 25 = 5 √ 36 = 6 √ 49 = 7 √ 64 = 8 √ 81 = 9 √ 100 = 10

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