Math  /  Numbers & Operations

Question\begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|l|}{ Transformez les chiffres périodiques suivants en fraction: } \\ \hline 0.6666.0.6666 \ldots .. & 1.2222.1.2222 \ldots \ldots .. & 1.3331.333 \ldots \ldots \\ \hline & & \\ \hline 0.454545450.45454545 \ldots \ldots. & 0.846153846153846153 & \\ \hline & & \\ \hline \end{tabular}

Studdy Solution
Solve each equation to find the fraction.
For 0.6666 0.6666\ldots : 9x=6 9x = 6 x=69=23 x = \frac{6}{9} = \frac{2}{3}
For 1.2222 1.2222\ldots : 9y=11 9y = 11 y=119 y = \frac{11}{9}
For 1.333 1.333\ldots : 9z=12 9z = 12 z=129=43 z = \frac{12}{9} = \frac{4}{3}
For 0.45454545 0.45454545\ldots : 99a=45 99a = 45 a=4599=511 a = \frac{45}{99} = \frac{5}{11}
For 0.846153846153 0.846153846153\ldots : 999999b=846153 999999b = 846153 b=846153999999=67 b = \frac{846153}{999999} = \frac{6}{7}
The fractions are: - 0.6666=23 0.6666\ldots = \frac{2}{3} - 1.2222=119 1.2222\ldots = \frac{11}{9} - 1.333=43 1.333\ldots = \frac{4}{3} - 0.45454545=511 0.45454545\ldots = \frac{5}{11} - 0.846153846153=67 0.846153846153\ldots = \frac{6}{7}

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