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Subtract $0.\overline{01}$ from 0.02 and express the result as a fraction.

 Jan 12, 2022
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Subtrahiere $0.\overline{01}$ von 0,02 und drücke das Ergebnis als Bruch aus.

 

Hello Guest!

 

\(0.02-0.\overline{01}=0.00\overline{98}\)

 

   \(0.009898\overline{98}\)  =    x

\(\underline{ 0.989898\overline{98}}\)  =  100x

\(-0.98\)               = - 49/50

 

\(x-100x=-\frac{49}{50}\\ -99x=-\frac{49}{50}\\ x=\dfrac{49}{99\cdot 50}=\dfrac{7^2}{3^2\cdot 11\cdot 5^2\cdot 2}\)

\(0.02-0.\overline{01}=\dfrac{49}{4950}\)

laugh  !

 Jan 12, 2022

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