Subtraction In Bars

4. 8 6 8 6 8 6 3. 9 5 9 5 9 5 0 \large{\begin{array}{ccccccccc} && 4.& 8 & 6& 8 & 6& 8 & 6&\ldots\\ -&& 3. & 9& 5& 9 & 5& 9 & 5&\ldots\\ \hline & & & & & & && &\phantom0\\ \hline \end{array}}

What is the value of the subtraction above?

0.919191 0.919191\ldots 0.9393939 0.9393939\ldots 0.909090 0.909090\ldots 0.9292929 0.9292929\ldots

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1 solution

Let x = 4. 86 . . . ( 1 ) x=4.\overline{86} \ ...(1) .

Multiplying by 100 100 .

100 x = 486. 86 . . . ( 2 ) \Rightarrow 100x=486.\overline{86} \ ...(2)

Subtracting ( 1 ) (1) from ( 2 ) (2) .

99 x = 482 \Rightarrow 99x=482

x = 482 99 \Rightarrow x=\color{#3D99F6}{\dfrac{482}{99}}

And y = 3. 95 . . . ( 3 ) y=3.\overline{95} \ ...(3) .

Multiplying by 100 100 .

100 y = 395. 95 . . . ( 4 ) \Rightarrow 100y=395.\overline{95} \ ...(4)

Subtracting ( 3 ) (3) from ( 4 ) (4) .

99 y = 392 \Rightarrow 99y=392

y = 392 99 \Rightarrow y=\color{#20A900}{\dfrac{392}{99}} .

x y = 482 99 392 99 = 90 99 = 0. 90 \therefore x-y=\color{#3D99F6}{\dfrac{482}{99}}-\color{#20A900}{\dfrac{392}{99}}=\dfrac{90}{99}=\boxed{0.\overline{90}}

Thanks for the amazing solution you've posted. :)

Sandeep Bhardwaj - 4 years, 10 months ago

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