Запишите рациональные числа в виде периодических дробей:
- $${\largeа)}\ {-}\frac{3}{7};$$
- $${\largeб)}\ \frac{9}{16};$$
- $${\largeв)}\ {-}\frac{511}{90};$$
- $${\largeг)}\ \frac{17}{99}.$$
Задание 103
Источник заимствования: Алгебра. 7 класс. Учебник для общеобразовательных организаций / С.М. Никольский, М.К. Потапов, Н.Н. Решетников, А.В. Шевкин – Просвещение, 2013. – 28 c. ISBN 978-5-09-027739-6
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Решение:
- $${\largeа)}\ {-}\frac{3}{7}={-}0{,}(428571)$$$$\phantom{\largeа)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}3\phantom{000000000}\\0\\\hline\end{array}\begin{array}{|l}7\\\hline0{,}428571428{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}30\\28\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}20\\14\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}60\\56\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}30\\28\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}-\begin{array}{r}20\\14\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}60\\56\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}40{...}\end{array}\end{array}$$
- $${\largeб)}\ \frac{9}{16}=0{,}5625(0)$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}9\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}16\\\hline0{,}5625\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}90\\80\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}100\\96\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}40\\32\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}80\\80\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$
- $${\largeв)}\ {-}\frac{511}{90}={-}5{,}6(7)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}511\phantom{0000}\\450\\\hline\end{array}\begin{array}{|l}90\\\hline5{,}6777{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}610\\540\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}700\\630\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}700\\630\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}700\\630\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}700{...}\end{array}\end{array}$$
- $${\largeг)}\ \frac{17}{99}=0{,}(17)$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}17\phantom{0000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}99\\\hline0{,}1717{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}170\\99\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}710\\693\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}170\\99\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}710\\693\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}170{...}\end{array}\end{array}$$