§ 2. Задание 105. «Алгебра. 7 класс. Учебник для общеобразовательных организаций» АЛГЕБРА 7 ГДЗ Задание 105

    Задание 105

    Запишите в виде рационального числа периодическую дробь:

      • $${\largeа)}\ {-}0{,}(3);$$
      • $${\largeб)}\ {-}1{,}(2);$$
      • $${\largeв)}\ {-}2{,}(5);$$
      • $${\largeг)}\ {-}0{,}(17);$$
      • $${\largeд)}\ {-}3{,}(18);$$
      • $${\largeе)}\ {-}1{,}(05);$$
      • $${\largeж)}\ 2{,}(0);$$
      • $${\largeз)}\ {-}0{,}(0);$$
      • $${\largeи)}\ 4{,}37(0).$$

    Источник заимствования: Алгебра. 7 класс. Учебник для общеобразовательных организаций / – Просвещение, 2013. – 28 c. ISBN 978-5-09-027739-6
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    Решение:

      • $${\largeа)}\ {-}0{,}(3)={-}\frac{1}{3};$$$$\phantom{\largeа)}\ x={-}0{,}(3)$$$$\phantom{\largeа)}\ 10x={-}3{,}(3)$$$$\phantom{\largeа)}\ 10x-x={-}3-({-}0)$$$$\phantom{\largeа)}\ 9x={-}3$$$$\phantom{\largeа)}\ x={-}\frac{3}{9}$$$$\phantom{\largeа)}\ x={-}\frac{1}{3}$$
      • $${\largeб)}\ {-}1{,}(2)={-}1\frac{2}{9};$$$$\phantom{\largeб)}\ x={-}1{,}(2)$$$$\phantom{\largeб)}\ 10x={-}12{,}(2)$$$$\phantom{\largeб)}\ 10x-x={-}12-({-}1)$$$$\phantom{\largeб)}\ 9x={-}11$$$$\phantom{\largeб)}\ x={-}\frac{11}{9}$$$$\phantom{\largeб)}\ x={-}1\frac{2}{9}$$
      • $${\largeв)}\ {-}2{,}(5)={-}2\frac{5}{9};$$$$\phantom{\largeв)}\ x={-}2{,}(5)$$$$\phantom{\largeв)}\ 10x={-}25{,}(5)$$$$\phantom{\largeв)}\ 10x-x={-}25-({-}2)$$$$\phantom{\largeв)}\ 9x={-}23$$$$\phantom{\largeв)}\ x={-}\frac{23}{9}$$$$\phantom{\largeв)}\ x={-}2\frac{5}{9}$$
      • $${\largeг)}\ {-}0{,}(17)={-}\frac{17}{99};$$$$\phantom{\largeг)}\ x={-}0{,}(17)$$$$\phantom{\largeг)}\ 100x={-}17{,}(17)$$$$\phantom{\largeг)}\ 100x-x={-}17-({-}0)$$$$\phantom{\largeг)}\ 99x={-}17$$$$\phantom{\largeг)}\ x={-}\frac{17}{99}$$
      • $${\largeд)}\ {-}3{,}(18)={-}3\frac{2}{11};$$$$\phantom{\largeд)}\ x={-}3{,}(18)$$$$\phantom{\largeд)}\ 100x={-}318{,}(18)$$$$\phantom{\largeд)}\ 100x-x={-}318-({-}3)$$$$\phantom{\largeд)}\ 99x={-}315$$$$\phantom{\largeд)}\ x={-}\frac{315}{99}$$$$\phantom{\largeд)}\ x={-}\frac{35}{11}$$$$\phantom{\largeд)}\ x={-}3\frac{2}{11}$$
      • $${\largeе)}\ {-}1{,}(05)={-}1\frac{5}{99};$$$$\phantom{\largeе)}\ x={-}1{,}(05)$$$$\phantom{\largeе)}\ 100x={-}105{,}(05)$$$$\phantom{\largeе)}\ 100x-x={-}105-({-}1)$$$$\phantom{\largeе)}\ 99x={-}104$$$$\phantom{\largeе)}\ x={-}\frac{104}{99}$$$$\phantom{\largeе)}\ x={-}1\frac{5}{99}$$
      • $${\largeж)}\ \vphantom{\frac{0}{0}}2{,}(0)=2;$$
      • $${\largeз)}\ \vphantom{\frac{0}{0}}{-}0{,}(0)=0;$$
      • $${\largeи)}\ 4{,}37(0)=4{,}37=4\frac{37}{100}.$$

    Задание 104Задание 106