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NSW Y8 Maths Working with Numbers Terminating and Recurring Decimals

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Terminating and Recurring Decimals Theory

All numbers in the form \(\frac{p}{q}\) can be expressed as terminating or recurring decimals, provided \(p\) and \(q\) are integers. \textbf{Example 1}\\ Convert the following to terminating on recurring decimals.\\ \textbf{i)} \(\dfrac{3}{8}\)\\ \textbf{ii)} \(\dfrac{2}{11}\)\\ \textbf{Example 1 solution}\\ \begin{multicols}{2} \textbf{i)} \(\longdivision{3}{8}\)\\ \columnbreak \textbf{ii)} \(\longdivision{2}{11}\)\\ \(\begin{aligned} \therefore \frac{12}{11} & =0.181818 \ldots \\ & =0.\dot{1}\dot{8} \end{aligned}\)\\ There is an interesting pattern for \(\frac{p}{11}\).\\ The repeating numbers always add to 9 \\ \(\dfrac{1}{11}=0.\dot{0}\dot{9}, \dfrac{2}{11}=0.\dot{1}\dot{8},\dfrac{3}{11}=\dot{2}\dot{7}\), etc \end{multicols}

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