Задание 85

Решение:

• $${\largeа)}\ \frac{1}{3}=0{,}333{...}=0{,}(3)$$$$\phantom{\largeа)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}1\phantom{000}\\0\\\hline\end{array}\begin{array}{|l}3\\\hline0{,}333{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}10\\9\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}10\\9\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}10\\9\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}10{...}\end{array}\end{array}$$
• $$\phantom{\largeа)}\ \frac{2}{9}=0{,}222{...}=0{,}(2)$$$$\phantom{\largeа)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}2\phantom{000}\\0\\\hline\end{array}\begin{array}{|l}9\\\hline0{,}222{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}20\\18\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}20\\18\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}20\\18\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}20{...}\end{array}\end{array}$$
• $$\phantom{\largeа)}\ \frac{12}{5}=2{,}4=2{,}4000{...}=2{,}4(0)$$$$\phantom{\largeа)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}12\phantom{0}\\10\\\hline\end{array}\begin{array}{|l}5\\\hline2{,}4\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}20\\20\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$
• $$\phantom{\largeа)}\ \vphantom{\frac{0}{0}}12=12{,}000{...}=12{,}(0)$$

• $${\largeб)}\ \frac{24}{30}=0{,}8=0{,}8000{...}=0{,}8(0)$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}24\phantom{0}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}30\\\hline0{,}8\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}240\\240\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$
• $$\phantom{\largeб)}\ \frac{36}{48}=0{,}75=0{,}75000{...}=0{,}75(0)$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}36\phantom{00}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}48\\\hline0{,}75\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}360\\336\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}240\\240\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}0\end{array}\end{array}$$
• $$\phantom{\largeб)}\ \frac{4}{7}=0{,}571428571{...}=0{,}(571428)$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}4\phantom{000000000}\\0\\\hline\end{array}\begin{array}{|l}7\\\hline0{,}571428571{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}30\\28\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}20\\14\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}60\\56\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}40\\35\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}-\begin{array}{r}50\\49\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}10\\7\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}30{...}\end{array}\end{array}$$
• $$\phantom{\largeб)}\ \frac{45}{63}=0{,}714285714{...}=0{,}(714285)$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}45\phantom{000000000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}63\\\hline0{,}714285714{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}450\\441\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}90\\63\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}270\\252\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}180\\126\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}540\\504\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}360\\315\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}450\\441\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}90\\63\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}270\\252\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}180{...}\end{array}\end{array}$$

• $${\largeв)}\ \frac{20}{41}=0{,}487804878{...}=0{,}(48780)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}20\phantom{000000000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}41\\\hline0{,}487804878{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}200\\164\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}360\\328\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}320\\287\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}330\\328\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}20\\0\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}200\\164\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}360\\328\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}-\begin{array}{r}320\\287\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}330\\328\\\hline\end{array}\end{array}\\\phantom{000000000000}\begin{array}{r}20{...}\end{array}\end{array}$$
• $$\phantom{\largeв)}\ \frac{15}{37}=0{,}405405405{...}=0{,}(405)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}15\phantom{000000000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}37\\\hline0{,}405405405{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}150\\148\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}20\\0\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}200\\185\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}150\\148\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}20\\0\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}200\\185\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}150\\148\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}20\\0\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}200\\185\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}150{...}\end{array}\end{array}$$
• $$\phantom{\largeв)}\ \frac{5}{21}=0{,}238095238{...}=0{,}(238095)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}5\phantom{000000000}\\0\\\hline\end{array}\begin{array}{|l}21\\\hline0{,}238095238{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}50\\42\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}80\\63\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}170\\168\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}20\\0\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}200\\189\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}110\\105\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}50\\42\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}-\begin{array}{r}80\\63\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}-\begin{array}{r}170\\168\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}20{...}\end{array}\end{array}$$
• $$\phantom{\largeв)}\ \frac{17}{42}=0{,}404761904{...}=0{,}4(047619)$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}17\phantom{000000000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}42\\\hline0{,}404761904{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}170\\168\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}20\\0\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}200\\168\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}320\\294\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}260\\252\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}80\\42\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}-\begin{array}{r}380\\378\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}20\\0\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}-\begin{array}{r}200\\168\\\hline\end{array}\end{array}\\\phantom{00000000000}\begin{array}{r}320{...}\end{array}\end{array}$$

• $${\largeг)}\ \frac{8}{9}=0{,}888{...}=0{,}(8)$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}8\phantom{000}\\0\\\hline\end{array}\begin{array}{|l}9\\\hline0{,}888{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}80\\72\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}80\\72\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}80\\72\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}80{...}\end{array}\end{array}$$
• $$\phantom{\largeг)}\ \frac{7}{9}=0{,}777{...}=0{,}(7)$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}7\phantom{000}\\0\\\hline\end{array}\begin{array}{|l}9\\\hline0{,}777{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}70\\63\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}70\\63\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}70\\63\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}70{...}\end{array}\end{array}$$
• $$\phantom{\largeг)}\ \frac{5}{9}=0{,}555{...}=0{,}(5)$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}5\phantom{000}\\0\\\hline\end{array}\begin{array}{|l}9\\\hline0{,}555{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}50\\45\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}50\\45\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}50\\45\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}50{...}\end{array}\end{array}$$
• $$\phantom{\largeг)}\ \frac{3}{9}=0{,}333{...}=0{,}(3)$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}3\phantom{000}\\0\\\hline\end{array}\begin{array}{|l}9\\\hline0{,}333{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}30\\27\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}30\\27\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}30\\27\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}30{...}\end{array}\end{array}$$

• $${\largeд)}\ \frac{13}{99}=0{,}1313{...}=0{,}(13)$$$$\phantom{\largeд)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}13\phantom{0000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}99\\\hline0{,}1313{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}130\\99\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}310\\297\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}130\\99\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}310\\297\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}130{...}\end{array}\end{array}$$
• $$\phantom{\largeд)}\ \frac{25}{99}=0{,}2525{...}=0{,}(25)$$$$\phantom{\largeд)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}25\phantom{0000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}99\\\hline0{,}2525{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}250\\198\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}520\\495\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}250\\198\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}520\\495\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}250{...}\end{array}\end{array}$$
• $$\phantom{\largeд)}\ \frac{71}{99}=0{,}7171{...}=0{,}(71)$$$$\phantom{\largeд)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}71\phantom{0000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}99\\\hline0{,}7171{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}710\\693\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}170\\99\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}710\\693\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}170\\99\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}710{...}\end{array}\end{array}$$
• $$\phantom{\largeд)}\ \frac{42}{99}=0{,}4242{...}=0{,}(42)$$$$\phantom{\largeд)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}42\phantom{0000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}99\\\hline0{,}4242{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}420\\396\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}240\\198\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}420\\396\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}240\\198\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}420{...}\end{array}\end{array}$$

• $${\largeе)}\ \frac{123}{999}=0{,}123123{...}=0{,}(123)$$$$\phantom{\largeе)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}123\phantom{000000}\\\phantom{00}0\\\hline\end{array}\begin{array}{|l}999\\\hline0{,}123123{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}1230\\999\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}2310\\1998\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}3120\\2997\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}1230\\999\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}2310\\1998\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}3120\\2997\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}1230{...}\end{array}\end{array}$$
• $$\phantom{\largeе)}\ \frac{12}{999}=0{,}012012{...}=0{,}(012)$$$$\phantom{\largeе)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}12\phantom{000000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}999\\\hline0{,}012012{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}120\\0\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}1200\\999\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}2010\\1998\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}120\\0\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}1200\\999\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}2010\\1998\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}120{...}\end{array}\end{array}$$
• $$\phantom{\largeе)}\ \frac{5}{999}=0{,}005005{...}=0{,}(005)$$$$\phantom{\largeе)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}5\phantom{000000}\\0\\\hline\end{array}\begin{array}{|l}999\\\hline0{,}005005{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}50\\0\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}500\\0\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}5000\\4995\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}50\\0\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}500\\0\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}5000\\4995\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}50{...}\end{array}\end{array}$$