Simplify

0.6666...+0.77777...+0.88888....+.33333... yields the result:
a-2(3/10)
b-2(2/3)
c-2.353535...
d-5(3/10)

Note by Mehdi Balti
3 years ago

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1 vote

  Easy Math Editor

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**bold** or __bold__ bold

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[example link](https://brilliant.org)example link
> This is a quote
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    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

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# 4 spaces, and now they show
# up as a code block.

print "hello world"
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Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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\(0.\dot{6} + 0.\dot{7} + 0.\dot{8} + 0.\dot{3} = \dfrac{6}{9} + \dfrac{7}{9} + \dfrac{8}{9} + \dfrac{3}{9} = \dfrac{6+7+8+3}{9} = \dfrac{24}{9} = \dfrac{8}{3} = 2\frac{2}{3}\)

Chew-Seong Cheong - 3 years ago

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Thanks buddy :)

Mehdi Balti - 3 years ago

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0.666...+0.777...+0.888...+0.3333...

let x=0.888..

100x=88.888..

minus the first two values

99x=88

x=(88/ 99 } =8/8

repeat steps for all values and you get

(2/3)+(7/9)+(8/9)+(1/3)

=(8/3)

=2(2/3)

Sorry don't know how to use LaTeX!

Raghav Arora - 3 years ago

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Thank you :)

Mehdi Balti - 3 years ago

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b

Mrinmay Dhar - 3 years ago

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Brilliant solution, couldn't have thought of a better way to solve it.

Raghav Arora - 3 years ago

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What you did there, I see it.

Mrinmay Dhar - 3 years ago

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Yeap got it well :)Thanks all of you

Mehdi Balti - 3 years ago

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Thanks dear :*

Mehdi Balti - 3 years ago

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