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If the base 8 decimal 0.30403...8 is equivalent to a/b, where a and b are relatively prime, express 2b - a in base 8.

 Oct 2, 2021
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What is this number?    0.30403...8

 

Do you mean that the number is repeating?    Is the number  0.3040 where the 3040 keeps repeating?   

And it is in base 8

 

If I have interpreted it correctly then

let  

10000x = 3040.30403040...   base 8

          x =       0.30403040...   base 8

 7777x = 3040   base 8

 

\(x=\frac{3040}{7777}\;\;base8\\ x=\frac{340}{1111}\;\;base8\\ \)

 

a= 340    and b=1111

2b = 2222

a   =   340

 

2b-a =   1662 (base 8)

 Oct 2, 2021

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