§ 2. Задание 45*. «Алгебра. Рабочая тетрадь. 7 класс. В 2 частях. Часть 1» АЛГЕБРА 7 ГДЗ Задание 45*

    Задание 45*

    Запишите периодическую дробь в виде обыкновенной дроби:

      • \(\begin{array}[t]{lll}\begin{array}{l}x=0{,}0(7),\\[0.9ex]x=0{,}0777{...},\\[0.9ex]10x=0{,}777{...},\\[0.9ex]100x=7{,}777{...},\\[0.9ex]100x-10x=7,\\[0.9ex]90x=7,\\[0.9ex]x=\frac{7}{90};\end{array}&&&\begin{array}{l}x=0{,}5(7),\\[0.9ex]x=0{,}5777{...},\\[0.9ex]10x=5{,}777{...},\\[0.9ex]100x=57{,}777{...},\\[0.9ex]100x-10x=52,\\[0.9ex]90x=52,\\[0.9ex]x=\frac{52}{90}.\end{array}\end{array}\)
      • \({\largeа)}\ x=0{,}0(25);\)
      • \({\largeб)}\ x=0{,}00(5);\)
      • \(\definecolor{dots}{RGB}{110,177,146}{\color{dots}{\large........................................................................}}\)
      • \({\color{dots}{\large........................................................................}}\)
      • \({\color{dots}{\large........................................................................}}\)
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      • \({\largeв)}\ x=0{,}12(4);\)
      • \({\largeг)}\ x=0{,}1(24).\)
      • \({\color{dots}{\large........................................................................}}\)
      • \({\color{dots}{\large........................................................................}}\)
      • \({\color{dots}{\large........................................................................}}\)
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    Источник заимствования: Алгебра. Рабочая тетрадь. 7 класс. В 2 частях. Часть 1 / – Просвещение, 2018. – 22 c. ISBN 978-5-09-051661-7
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    Решение:

      • \({\largeа)}\ x=0{,}0(25),\)
        \(\phantom{\largeа)}\ x=0{,}0252525{...},\)
        \(\phantom{\largeа)}\ 10x=0{,}252525{...},\)
        \(\phantom{\largeа)}\ 1000x=25{,}252525{...},\)
        \(\phantom{\largeа)}\ 1000x-10x=25,\)
        \(\phantom{\largeа)}\ 990x=25,\)
        \(\phantom{\largeа)}\ x=\frac{25}{990};\)
      • \({\largeб)}\ x=0{,}00(5),\)
        \(\phantom{\largeб)}\ x=0{,}00555{...},\)
        \(\phantom{\largeб)}\ 100x=0{,}555{...},\)
        \(\phantom{\largeб)}\ 1000x=5{,}555{...},\)
        \(\phantom{\largeб)}\ 1000x-100x=5,\)
        \(\phantom{\largeб)}\ 900x=5,\)
        \(\phantom{\largeб)}\ x=\frac{5}{900};\)
      • \({\largeв)}\ x=0{,}12(4),\)
        \(\phantom{\largeв)}\ x=0{,}12444{...},\)
        \(\phantom{\largeв)}\ 100x=12{,}444{...},\)
        \(\phantom{\largeв)}\ 1000x=124{,}444{...},\)
        \(\phantom{\largeв)}\ 1000x-100x=112,\)
        \(\phantom{\largeв)}\ 900x=112,\)
        \(\phantom{\largeв)}\ x=\frac{112}{900};\)
      • \({\largeг)}\ x=0{,}1(24),\)
        \(\phantom{\largeг)}\ x=0{,}1242424{...},\)
        \(\phantom{\largeг)}\ 10x=1{,}242424{...},\)
        \(\phantom{\largeг)}\ 1000x=124{,}242424{...},\)
        \(\phantom{\largeг)}\ 1000x-10x=123,\)
        \(\phantom{\largeг)}\ 990x=123,\)
        \(\phantom{\largeг)}\ x=\frac{123}{990}.\)

    Задание 44Задание 46*