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find-two-irrational-numbers-between-0-333-and-0-444-




Question Number 141997 by jlewis last updated on 25/May/21
find two irrational numbers   between 0.333.... and 0.444...
findtwoirrationalnumbersbetween0.333.and0.444
Answered by MJS_new last updated on 25/May/21
.33312345678910111213...  (1/e)≈.367879441...
.333123456789101112131e.367879441
Commented by MJS_new last updated on 25/May/21
.333000333300003333300000...
.333000333300003333300000
Commented by jlewis last updated on 25/May/21
wah! i have not gotten how u   arrived to this
wah!ihavenotgottenhowuarrivedtothis
Commented by MJS_new last updated on 25/May/21
easy: invent an infinite non−periodic pattern  .01 001 0001 00001 000001...  .0 1 2 3 4 5 6 7 8 9 10 11 12...  .1 4 9 16 25 36 49 64 81 100...  .2 4 8 16 32 64 128 256 512...  .0 1 1 2 3 5 8 13 21 34 55 89...
easy:inventaninfinitenonperiodicpattern.01001000100001000001.0123456789101112.149162536496481100.248163264128256512.01123581321345589
Commented by jlewis last updated on 25/May/21
 i get it now.thanks
igetitnow.thanks
Answered by MJS_new last updated on 25/May/21
you could also do this:  .333...=(3/9)  .444...=(4/9)  ((((3/9))^2 ×(4/9)))^(1/3) =((4/(81)))^(1/3) ≈.366880805...∉Q  (√((3/9)×(4/9)))=((2(√3))/9)≈.384900179...∉Q  (((3/9)×((4/9))^3 ))^(1/4) =(((192))^(1/4) /9)≈.413602159...∉Q
youcouldalsodothis:.333=39.444=49(39)2×493=4813.366880805Q39×49=239.384900179Q39×(49)34=19249.413602159Q

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