§ 2. Задание 104. «Алгебра. 7 класс. Учебник для общеобразовательных организаций» АЛГЕБРА 7 ГДЗ Задание 104

    Задание 104

    Запишите рациональные числа в виде периодических дробей:

      • $${\largeа)}\ {-}\frac{1}{2};\ 0;\ {-}1{,}24;$$
      • $${\largeб)}\ \frac{1}{3};\ {-}\frac{4}{7};\ {-}2\frac{5}{13};$$
      • $${\largeв)}\ 2\frac{24}{33};\ {-}\frac{120}{210};\ \frac{57}{16};$$
      • $${\largeг)}\ {-}\frac{21}{90};\ 1\frac{16}{90};\ {-}3\frac{4}{7}.$$

    Источник заимствования: Алгебра. 7 класс. Учебник для общеобразовательных организаций / – Просвещение, 2013. – 28 c. ISBN 978-5-09-027739-6
    Реклама
    А+АА-

    Решение:

      • $${\largeа)}\ {-}\frac{1}{2}={-}0{,}5={-}0{,}5(0)$$
      • $$\phantom{\largeа)}\ \vphantom{\frac{0}{0}}0=0{,}(0)$$
      • $$\phantom{\largeа)}\ \vphantom{\frac{0}{0}}{-}1{,}24={-}1{,}24(0)$$

      • $${\largeб)}\ \frac{1}{3}=0{,}(3)$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}1\phantom{000}\\0\\\hline\end{array}\begin{array}{|l}3\\\hline0{,}333{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}10\\9\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}10\\9\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}10\\9\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}10{...}\end{array}\end{array}$$
      • $$\phantom{\largeб)}\ {-}\frac{4}{7}={-}0{,}(571428)$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}4\phantom{000000000}\\0\\\hline\end{array}\begin{array}{|l}7\\\hline0{,}571428571{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}30\\28\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}20\\14\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}60\\56\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}30{...}\end{array}\end{array}$$
      • $$\phantom{\largeб)}\ {-}2\frac{5}{13}={-}2{,}(384615)$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}5\phantom{000000000}\\0\\\hline\end{array}\begin{array}{|l}13\\\hline0{,}384615384{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}50\\39\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}110\\104\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}60\\52\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}80\\78\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}20\\13\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}70\\65\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}50\\39\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}110\\104\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}60\\52\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}80{...}\end{array}\end{array}$$

      • $${\largeв)}\ 2\frac{24}{33}=2\frac{8}{11}=2{,}(72)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}8\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}11\\\hline0{,}7272{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}80\\77\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}30\\22\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}80\\77\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}30\\22\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}80{...}\end{array}\end{array}$$
      • $$\phantom{\largeв)}\ {-}\frac{120}{210}={-}\frac{4}{7}={-}0{,}(571428)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}4\phantom{000000000}\\0\\\hline\end{array}\begin{array}{|l}7\\\hline0{,}571428571{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}30\\28\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}20\\14\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}60\\56\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}30{...}\end{array}\end{array}$$
      • $$\phantom{\largeв)}\ \frac{57}{16}=3\frac{9}{16}=3{,}5625(0)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}9\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}16\\\hline0{,}5625\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}90\\80\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}100\\96\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}40\\32\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}80\\80\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$

      • $${\largeг)}\ {-}\frac{21}{90}={-}\frac{7}{30}={-}0{,}2(3)$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}7\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}30\\\hline0{,}2333{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}70\\60\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}100\\90\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}100\\90\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}100\\90\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}100{...}\end{array}\end{array}$$
      • $$\phantom{\largeг)}\ 1\frac{16}{90}=1\frac{8}{45}=1{,}1(7)$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}8\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}45\\\hline0{,}1777{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}80\\45\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}350\\315\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}350\\315\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}350\\315\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}350{...}\end{array}\end{array}$$
      • $$\phantom{\largeг)}\ {-}3\frac{4}{7}={-}3{,}(571428)$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}4\phantom{000000000}\\0\\\hline\end{array}\begin{array}{|l}7\\\hline0{,}571428571{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}30\\28\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}20\\14\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}60\\56\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}30{...}\end{array}\end{array}$$