Задание 160

Выполните задания $158-159$, округлив данные в них числа до третьей значащей цифры.

Источник заимствования: Алгебра. 7 класс. Учебник для общеобразовательных организаций / С.М. Никольский, М.К. Потапов, Н.Н. Решетников, А.В. Шевкин – Просвещение, 2013. – 42 c. ISBN 978-5-09-027739-6

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Решение:

Задание $\textbf{158}$:

$${\largeа)}\ 2{,}35\cdot3{,}251\approx2{,}35\cdot3{,}25\approx7{,}6375\approx7{,}64$$

$$\begin{array}{r}\times\begin{array}{r}2{,}35\\3{,}25\\\hline\end{array}\phantom{0}\\\begin{array}{r}+\begin{array}{r}1175\\470\phantom{0}\\705\phantom{00}\\\hline\end{array}\\\begin{array}{r}7{,}6375\end{array}\end{array}\end{array}$$

$${\largeб)}\ {-}4{,}3205\cdot2{,}503\approx{-}4{,}32\cdot2{,}50\approx{-}10{,}8$$

$$\begin{array}{r}\times\begin{array}{r}4{,}32\\2{,}5\\\hline\end{array}\phantom{0}\\\begin{array}{r}+\begin{array}{r}2160\\864\phantom{0}\\\hline\end{array}\\\begin{array}{r}10{,}800\end{array}\end{array}\end{array}$$

$${\largeв)}\ 3\cdot2{,}(1)=3\cdot2{,}111{...}\approx3\cdot2{,}11\approx6{,}33$$

$$\begin{array}{r}\times\begin{array}{r}2{,}11\\3\\\hline\end{array}\\\begin{array}{r}6{,}33\end{array}\end{array}$$

$${\largeг)}\ 0{,}56\cdot0{,}(3)=0{,}56\cdot0{,}3333{...}\approx0{,}56\cdot0{,}333\approx0{,}18648\approx0{,}186$$

$$\begin{array}{r}\times\begin{array}{r}0{,}333\\0{,}56\\\hline\end{array}\phantom{0}\\\begin{array}{r}+\begin{array}{r}1998\\1665\phantom{0}\\\hline\end{array}\\\begin{array}{r}0{,}18648\end{array}\end{array}\end{array}$$

$${\largeд)}\ 0{,}(1)\cdot0{,}(2)=0{,}1111{...}\cdot0{,}2222{...}\approx0{,}111\cdot0{,}222\approx0{,}024642\approx0{,}0246$$

$$\begin{array}{r}\times\begin{array}{r}0{,}111\\0{,}222\\\hline\end{array}\phantom{0}\\\begin{array}{r}+\begin{array}{r}222\\222\phantom{0}\\222\phantom{00}\\\hline\end{array}\\\begin{array}{r}0{,}024642\end{array}\end{array}\end{array}$$

$${\largeе)}\ 12{,}(45)\cdot10{,}(1)=12{,}4545{...}\cdot10{,}1111{...}\approx12{,}5\cdot10{,}1\approx126{,}25\approx126$$

$$\begin{array}{r}\times\begin{array}{r}12{,}5\\10{,}1\\\hline\end{array}\phantom{0}\\\begin{array}{r}+\begin{array}{r}125\\125\phantom{00}\\\hline\end{array}\\\begin{array}{r}126{,}25\end{array}\end{array}\end{array}$$

Задание $\textbf{159}$:

$${\largeа)}\ 3{,}57:0{,}259\approx3{,}57:0{,}259\approx3570:259\approx13{,}783{...}\approx13{,}8$$

$$\begin{array}{l}\begin{array}{r}-\begin{array}{l}3570\phantom{000}\\259\\\hline\end{array}\begin{array}{|l}259\\\hline13{,}783{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}980\\777\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}2030\\1813\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}2170\\2072\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}980\\777\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}2030{...}\end{array}\end{array}$$

$${\largeб)}\ {-}3{,}28:40{,}12\approx{-}3{,}28:40{,}1\approx{-}32{,}8:401\approx{-}0{,}08179{...}\approx{-}0{,}0818$$

$$\begin{array}{l}\begin{array}{r}-\begin{array}{l}32{,}8\phantom{0000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}401\\\hline0{,}08179{...}\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}328\\0\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}3280\\3208\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}720\\401\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}3190\\2807\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}3830\\3609\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}2210{...}\end{array}\end{array}$$

$${\largeв)}\ 12:0{,}(1)=12:0{,}1111{...}\approx12:0{,}111\approx12\ 000:111\approx108{,}108{...}\approx108$$

$$\begin{array}{l}\begin{array}{r}-\begin{array}{l}12000\phantom{000}\\111\\\hline\end{array}\begin{array}{|l}111\\\hline108{,}108{...}\end{array}\\\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}90\\0\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}900\\888\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}120\\111\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}90\\0\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}-\begin{array}{r}900\\888\\\hline\end{array}\end{array}\\\phantom{00000000}\begin{array}{r}120{...}\end{array}\end{array}$$

$${\largeг)}\ 0{,}(2):2=0{,}2222{...}:2\approx0{,}222:2\approx0{,}111$$

$$\begin{array}{l}\begin{array}{r}-\begin{array}{l}0{,}222\\0\\\hline\end{array}\begin{array}{|l}2\\\hline0{,}111\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}2\\2\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}2\\2\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}2\\2\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}0\end{array}\end{array}$$

$${\largeд)}\ 4{,}(2):1{,}(3)=4{,}2222{...}:1{,}3333{...}\approx4{,}22:1{,}33\approx422:133\approx3{,}1729{...}\approx3{,}17$$

$$\begin{array}{l}\begin{array}{r}-\begin{array}{l}422\phantom{0000}\\399\\\hline\end{array}\begin{array}{|l}133\\\hline3{,}1729{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}230\\133\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}970\\931\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}390\\266\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}1240\\1197\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}430{...}\end{array}\end{array}$$

$${\largeе)}\ 45{,}6(12):10{,}(2)=45{,}61212{...}:10{,}222{...}\approx45{,}6:10{,}2\approx456:102\approx4{,}4705{...}\approx4{,}47$$

$$\begin{array}{l}\begin{array}{r}-\begin{array}{l}456\phantom{0000}\\408\\\hline\end{array}\begin{array}{|l}102\\\hline4{,}4705{...}\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}480\\408\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}720\\714\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}60\\0\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}-\begin{array}{r}600\\510\\\hline\end{array}\end{array}\\\phantom{0000000}\begin{array}{r}900{...}\end{array}\end{array}$$

Задание 159Задание 161