Задание 43

Запишите обыкновенную дробь в виде периодической дроби:

\(\begin{array}[t]{ll}\begin{array}{l}\phantom{\ }\frac{1}{3}=\frac{3}{9}=0{,}(3);\\[0.9ex]\frac{3}{11}=\frac{27}{99}=0{,}(27);\\[0.9ex]\frac{5}{90}=0{,}0(5)\\[0.1ex]\end{array}&&&\begin{array}{l}\\\begin{array}{l}5{,}000{...}\\450\\\hline\end{array}\begin{array}{|l}90\\\hline0{,}0555{...}\\\end{array}\\\phantom{0}\begin{array}{r}500\\450\\\hline\end{array}\\\phantom{00}\begin{array}{l}500\\{...}\end{array}\end{array}\end{array}\)

\({\largeа)}\ \frac{2}{11}=\phantom{\ .}\definecolor{dots}{RGB}{110,177,146}\color{dots}{\large....................}\)
\({\largeб)}\ \frac{10}{11}=\phantom{0}\color{dots}{\large....................}\)

\({\largeв)}\ \frac{5}{33}=\phantom{0}\color{dots}{\large....................}\)
\({\largeг)}\ \frac{28}{33}=\phantom{0}\color{dots}{\large....................}\)

\({\largeд)}\ \frac{7}{90}=\phantom{0}\color{dots}{\large....................}\)
\({\largeе)}\ \frac{8}{90}=\phantom{0}\color{dots}{\large....................}\)

\({\largeж)}\ \frac{23}{990}=\phantom{\ }\color{dots}{\large...................}\)
\({\largeз)}\ \frac{125}{999}=\phantom{0}\color{dots}{\large...................}\)

Источник заимствования: Алгебра. Рабочая тетрадь. 7 класс. В 2 частях. Часть 1 / М.К. Потапов, А.В. Шевкин – Просвещение, 2018. – 20 c. ISBN 978-5-09-051661-7

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Решение:

\({\largeа)}\ \frac{2}{11}=\frac{18}{99}=0{,}(18);\)
\({\largeб)}\ \frac{10}{11}=\frac{90}{99}=0{,}(90);\)

\({\largeв)}\ \frac{5}{33}=\frac{15}{99}=0{,}(15);\)
\({\largeг)}\ \frac{28}{33}=\frac{84}{99}=0{,}(84);\)

\({\largeд)}\ \frac{7}{90}=0{,}0(7);\)
\(\phantom{0000}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}7{,}0000{...}\\630\\\hline\end{array}\begin{array}{|l}90\\\hline0{,}0777{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}700\\630\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{l}700\\{...}\end{array}\end{array}\end{array}\)
\({\largeе)}\ \frac{8}{90}=0{,}0(8);\)
\(\phantom{0000}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}8{,}0000{...}\\720\\\hline\end{array}\begin{array}{|l}90\\\hline0{,}0888{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}800\\720\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{l}800\\{...}\end{array}\end{array}\end{array}\)

\({\largeж)}\ \frac{23}{990}=0{,}0(23);\)
\({\largeз)}\ \frac{125}{999}=0{,}(125).\)

Задание 42Задание 44