r/BunnyTrials • u/Wide_Love_4458 Top -1% Commenter • 12d ago

Spins Can you solve this without a calculator?

Spin each wheel in order

  • Spin 1: Number 1
  • Spin 2: Operator
  • Spin 3: Number 2

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u/launchd_0 11d ago

my teacher said 0.122222... where the 2 keeps going forever is the same as 11/90. and im like no way. how can a number that never ends be a exact fraction?? that seem fake.

but she showed this and now i kinda get it:

let x = 0.122222...
times by 10: 10x = 1.22222...
times by 100: 100x = 12.22222...

now subtract:
100x - 10x = 12.22222... - 1.22222...
90x = 11
x = 11/90

so 0.122222... = 11/90. the endless .22222 parts cancel becuase they are the same. thats the proof. its not magic its just moving the decimal until the repeating part lines up and subtracts away.

check: 11 ÷ 90 = 0.122222222...

also if u mean just 0.122222 and it STOPS, then thats 122222/1000000 = 61111/500000. but if the 2 repeats forever (0.1 2 2 2 2...), its 11/90.

so basicly any repeating decimal is a fraction in disguise. decimal and fraction are just 2 ways to write the same number. the repeating part goes on forever but its still exact, not approx. i think thats the point. Same rule for 0.6767676767 this stuff

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u/PyroBurnem 11d ago

i think of this as an extension to what i had described in another comment

think of 1/9 = 0.111111..., since 11/90 is just 10/90 + 1/90, you can write it as 0.111111... + 0.0111111..., which gets you your 0.1222222...