§ 2. Задание 41. «Алгебра. Рабочая тетрадь. 7 класс. В 2 частях. Часть 1» АЛГЕБРА 7 ГДЗ Задание 41

    Задание 41

    Запишите в виде периодической дроби число:

      • \(\begin{array}[t]{ll}\frac{1}{2}=\frac{5}{10}=0{,}5=0{,}5(0);&&&4=4{,}(0);\\\begin{array}{}\frac{2}{3}=0{,}666{...}=0{,}(6)\\[10.9ex]\\\end{array}&&&\begin{array}{l}\\\begin{array}{l}2{,}000{...}\\18\\\hline\end{array}\begin{array}{|l}3\\\hline0{,}666{...}\\\end{array}\\\phantom{0}\begin{array}{r}20\\18\\\hline\end{array}\\\phantom{00}\begin{array}{l}20\\{...}\end{array}\end{array}\end{array}\)
      • \({\largeа)}\ 7=\phantom{\ .}\definecolor{dots}{RGB}{110,177,146}\color{dots}{\large.....................}\)
      • \({\largeб)}\ 8{,}3=\phantom{0}\color{dots}{\large...................}\)
      • \({\largeв)}\ \frac{2}{9}=\phantom{0}\color{dots}{\large....................}\)
      • \({\largeг)}\ \frac{4}{9}=\phantom{0}\color{dots}{\large....................}\)
      • \({\largeд)}\ \frac{25}{99}=\phantom{0}\color{dots}{\large...................}\)
      • \({\largeе)}\ \frac{17}{99}=\phantom{0}\color{dots}{\large...................}\)

    Источник заимствования: Алгебра. Рабочая тетрадь. 7 класс. В 2 частях. Часть 1 / – Просвещение, 2018. – 19 c. ISBN 978-5-09-051661-7
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    Решение:

      • \({\largeа)}\ 7=7{,}(0);\)
      • \({\largeб)}\ 8{,}3=8{,}3(0);\)
      • \({\largeв)}\ \frac{2}{9}=0{,}222{...}=0{,}(2);\)
        \(\phantom{0000}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}2{,}000{...}\\18\\\hline\end{array}\begin{array}{|l}9\\\hline0{,}222{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}20\\18\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{l}20\\{...}\end{array}\end{array}\end{array}\)
      • \({\largeг)}\ \frac{4}{9}=0{,}444{...}=0{,}(4);\)
        \(\phantom{0000}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}4{,}000{...}\\36\\\hline\end{array}\begin{array}{|l}9\\\hline0{,}444{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}40\\36\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{l}40\\{...}\end{array}\end{array}\end{array}\)
      • \({\largeд)}\ \frac{25}{99}=0{,}2525{...}=0{,}(25);\)
        \(\phantom{0000}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}25{,}0000{...}\\198\\\hline\end{array}\begin{array}{|l}99\\\hline0{,}2525{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}520\\495\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}250\\198\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{l}520\\{...}\end{array}\end{array}\end{array}\)
      • \({\largeе)}\ \frac{17}{99}=0{,}1717{...}=0{,}(17).\)
        \(\phantom{0000}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}17{,}0000{...}\\\phantom{0}99\\\hline\end{array}\begin{array}{|l}99\\\hline0{,}1717{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}710\\693\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}170\\99\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{l}710\\{...}\end{array}\end{array}\end{array}\)