Найдите десятичное разложение обыкновенной дроби:
- $${\largeа)}\ \frac{4}{9};$$
- $${\largeб)}\ \frac{17}{25};$$
- $${\largeв)}\ \frac{689}{4950};$$
- $${\largeг)}\ \frac{5}{16}.$$
Задание 92
Источник заимствования: Алгебра. 7 класс. Учебник для общеобразовательных организаций / С.М. Никольский, М.К. Потапов, Н.Н. Решетников, А.В. Шевкин – Просвещение, 2013. – 26 c. ISBN 978-5-09-027739-6
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Решение:
- $${\largeа)}\ \frac{4}{9}=0{,}(4)$$$$\phantom{\largeа)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}4\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}9\\\hline0{,}4444{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}40\\36\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}40\\36\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}40\\36\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}40\\36\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}40{...}\end{array}\end{array}$$
- $${\largeб)}\ \frac{17}{25}=0{,}68$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}17\phantom{00}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}25\\\hline0{,}68\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}170\\150\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}200\\200\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}0\end{array}\end{array}$$
- $${\largeв)}\ \frac{689}{4950}=0{,}13(91)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}689\phantom{0000000}\\\phantom{00}0\\\hline\end{array}\begin{array}{|l}4950\\\hline0{,}1391919{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}6890\\4950\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}19400\\14850\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}45500\\44550\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}9500\\4950\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}45500\\44550\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}9500\\4950\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}45500\\44550\\\hline\end{array}\end{array}\\\phantom{000000000}\begin{array}{r}9500{...}\end{array}\end{array}$$
- $${\largeг)}\ \frac{5}{16}=0{,}3125$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}5\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}16\\\hline0{,}3125\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}50\\48\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}20\\16\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}40\\32\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}80\\80\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$