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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
2 years, 3 months ago

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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 - 2 years, 3 months ago

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Thanks buddy :)

Mehdi Balti - 2 years, 3 months 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 - 2 years, 3 months ago

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Thank you :)

Mehdi Balti - 2 years, 3 months ago

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b

Mrinmay Dhar - 2 years, 3 months ago

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

Raghav Arora - 2 years, 3 months ago

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What you did there, I see it.

Mrinmay Dhar - 2 years, 3 months ago

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Yeap got it well :)Thanks all of you

Mehdi Balti - 2 years, 3 months ago

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Thanks dear :*

Mehdi Balti - 2 years, 3 months ago

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