Реши номер 3 и 4

Краткий ответ

№ 3:

1. \(0,(6)=\dfrac{2}{3}\)
2. \(1,(55)=\dfrac{14}{9}\)
3. \(0,1(2)=\dfrac{11}{90}\)
4. \(-0,(8)=-\dfrac{8}{9}\)
5. \(-3,(27)=-\dfrac{36}{11}\)
6. \(-2,3(82)=-\dfrac{2359}{990}\)

№ 4:

1. \(4\)
2. \(\dfrac{19}{4}=4\dfrac{3}{4}\)

Решение

В скобках указана повторяющаяся часть десятичной дроби.

№ 3

1. \[ 0,(6)=\frac{6}{9}=\frac{2}{3}. \]

2. \[ 1,(55)=1+\frac{55}{99} =1+\frac{5}{9} =\frac{14}{9}. \]

3. Для смешанной периодической дроби: \[ 0,1(2)=\frac{12-1}{90}=\frac{11}{90}. \]

4. \[ -0,(8)=-\frac{8}{9}. \]

5. \[ -3,(27)=-\left(3+\frac{27}{99}\right) =-\left(3+\frac{3}{11}\right) =-\frac{36}{11}. \]

6. \[ 2,3(82)=2+\frac{382-3}{10\cdot99} =2+\frac{379}{990} =\frac{2359}{990}. \] Значит, \[ -2,3(82)=-\frac{2359}{990}. \]

№ 4

1. \[ (20,88:18+45:0,36):(19,59+11,95) \]

\[ 20,88:18=1,16,\qquad 45:0,36=125. \]

\[ 1,16+125=126,16, \] \[ 19,59+11,95=31,54. \]

\[ 126,16:31,54=4, \] так как \(31,54\cdot4=126,16\).

2. \[ \frac{7}{36}\cdot9+8\cdot\frac{11}{32} +\frac{9}{10}\cdot\frac{5}{18} \]

\[ \frac{7}{36}\cdot9=\frac74,\qquad 8\cdot\frac{11}{32}=\frac{11}{4},\qquad \frac{9}{10}\cdot\frac{5}{18}=\frac14. \]

\[ \frac74+\frac{11}{4}+\frac14 =\frac{19}{4} =4\frac34. \]