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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
1 year, 6 months ago

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$$0.\dot{6} + 0.\dot{7} + 0.\dot{8} + 0.\dot{3} = \dfrac{6}{9} + \dfrac{7}{9} + \dfrac{8}{9} + \dfrac{3}{9} = \dfrac{6+7+8+3}{9} = \dfrac{24}{9} = \dfrac{8}{3} = 2\frac{2}{3}$$ · 1 year, 6 months ago

Thanks buddy :) · 1 year, 6 months ago

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! · 1 year, 6 months ago

Thank you :) · 1 year, 6 months ago

b · 1 year, 6 months ago

Brilliant solution, couldn't have thought of a better way to solve it. · 1 year, 6 months ago

What you did there, I see it. · 1 year, 6 months ago

Yeap got it well :)Thanks all of you · 1 year, 6 months ago