§ 2. Задание 44. «Алгебра. Рабочая тетрадь. 7 класс. В 2 частях. Часть 1» АЛГЕБРА 7 ГДЗ Задание 44

    Задание 44

    Запишите периодическую дробь в виде обыкновенной дроби:

      • \(\begin{array}[t]{lll}\begin{array}{l}x=0{,}(1),\\[0.9ex]x=0{,}111{...},\\[0.9ex]10x=1{,}111{...},\\[0.9ex]10x-x=1,\\[0.9ex]9x=1,\\[0.9ex]x=\frac{1}{9};\end{array}&&&\begin{array}{l}x=0{,}(13),\\[0.9ex]x=0{,}131313{...},\\[0.9ex]100x=13{,}131313{...},\\[0.9ex]100x-x=13,\\[0.9ex]99x=13,\\[0.9ex]x=\frac{13}{99};\end{array}&&&\begin{array}{l}x=0{,}(751),\\[0.9ex]x=0{,}751751{...},\\[0.9ex]1000x=751{,}751751{...},\\[0.9ex]1000x-x=751,\\[0.9ex]999x=751,\\[0.9ex]x=\frac{751}{999}.\end{array}\end{array}\)
      • \({\largeа)}\ x=0{,}(2);\)
      • \({\largeб)}\ x=0{,}(3);\)
      • \({\largeв)}\ x=0{,}(14);\)
      • \(\definecolor{dots}{RGB}{110,177,146}{\color{dots}{\large........................................................................}}\)
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      • \({\largeг)}\ x=0{,}(43);\)
      • \({\largeд)}\ x=0{,}(359);\)
      • \({\largeе)}\ x=0{,}(740).\)
      • \({\color{dots}{\large........................................................................}}\)
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    Источник заимствования: Алгебра. Рабочая тетрадь. 7 класс. В 2 частях. Часть 1 / – Просвещение, 2018. – 21 c. ISBN 978-5-09-051661-7
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    Решение:

      • \({\largeа)}\ x=0{,}(2),\)
        \(\phantom{\largeа)}\ x=0{,}222{...},\)
        \(\phantom{\largeа)}\ 10x=2{,}222{...},\)
        \(\phantom{\largeа)}\ 10x-x=2,\)
        \(\phantom{\largeа)}\ 9x=2,\)
        \(\phantom{\largeа)}\ x=\frac{2}{9};\)
      • \({\largeб)}\ x=0{,}(3),\)
        \(\phantom{\largeб)}\ x=0{,}333{...},\)
        \(\phantom{\largeб)}\ 10x=3{,}333{...},\)
        \(\phantom{\largeб)}\ 10x-x=3,\)
        \(\phantom{\largeб)}\ 9x=3,\)
        \(\phantom{\largeб)}\ x=\frac{3}{9};\)
      • \({\largeв)}\ x=0{,}(14),\)
        \(\phantom{\largeв)}\ x=0{,}141414{...},\)
        \(\phantom{\largeв)}\ 100x=14{,}141414{...},\)
        \(\phantom{\largeв)}\ 100x-x=14,\)
        \(\phantom{\largeв)}\ 99x=14,\)
        \(\phantom{\largeв)}\ x=\frac{14}{99};\)
      • \({\largeг)}\ x=0{,}(43),\)
        \(\phantom{\largeг)}\ x=0{,}434343{...},\)
        \(\phantom{\largeг)}\ 100x=43{,}434343{...},\)
        \(\phantom{\largeг)}\ 100x-x=43,\)
        \(\phantom{\largeг)}\ 99x=43,\)
        \(\phantom{\largeг)}\ x=\frac{43}{99};\)
      • \({\largeд)}\ x=0{,}(359),\)
        \(\phantom{\largeд)}\ x=0{,}359359{...},\)
        \(\phantom{\largeд)}\ 1000x=359{,}359359{...},\)
        \(\phantom{\largeд)}\ 1000x-x=359,\)
        \(\phantom{\largeд)}\ 999x=359,\)
        \(\phantom{\largeд)}\ x=\frac{359}{999};\)
      • \({\largeе)}\ x=0{,}(740),\)
        \(\phantom{\largeе)}\ x=0{,}740740{...},\)
        \(\phantom{\largeе)}\ 1000x=740{,}740740{...},\)
        \(\phantom{\largeе)}\ 1000x-x=740,\)
        \(\phantom{\largeе)}\ 999x=740,\)
        \(\phantom{\largeе)}\ x=\frac{740}{999}.\)

    Задание 43Задание 45*