Представьте число 0,(8) в виде обыкновенной дроби.

1) $0,(8) = \frac{8}{9}$ 2) $0,2(35) = \frac{235-2}{990} = \frac{233}{990}$ 3) $0,(5) = \frac{5}{9}$ 4) $3,(27) = 3\frac{27}{99} = 3\frac{3}{11} = \frac{36}{11}$ 5) $0,5(8) = \frac{58-5}{90} = \frac{53}{90}$ 6) $28,10(01) = 28\frac{1001-10}{9900} = 28\frac{991}{9900}$ 7) $4,4(35) = 4\frac{435-4}{990} = 4\frac{431}{990}$ 8) $0,42(6) = \frac{426-42}{900} = \frac{384}{900} = \frac{32}{75}$ 9) $0,0(25) = \frac{25}{990}$ 10) $2,3(16) = 2\frac{316-3}{990} = 2\frac{313}{990}$ 11) $24,23(5) = 24\frac{235-23}{900} = 24\frac{212}{900} = 24\frac{53}{225}$ 12) $0,2(4) = \frac{24-2}{90} = \frac{22}{90} = \frac{11}{45}$ 13) $167,(89) = 167\frac{89}{99}$ 14) $1,1(19) = 1\frac{119-1}{990} = 1\frac{118}{990} = 1\frac{59}{495}$ 15) $25,(18) = 25\frac{18}{99} = 25\frac{2}{11} = \frac{277}{11}$ 16) $1,0189(12) = 1\frac{1018912-10189}{990000} = 1\frac{1008723}{990000}$ 17) $0,23(145) = \frac{23145-23}{99900} = \frac{23122}{99900} = \frac{11561}{49950}$ 18) $2,191(78) = 2\frac{19178-191}{99000} = 2\frac{19017}{99000} = 2\frac{6339}{33000} = 2\frac{2113}{11000}$ 19) $10,9(1) = 10\frac{91-9}{90} = 10\frac{82}{90} = 10\frac{41}{45} = \frac{491}{45}$ 20) $1,(009) = 1\frac{9}{999} = 1\frac{1}{111} = \frac{112}{111}$ 21) $9,990(001) = 9\frac{990001-990}{999000} = 9\frac{989011}{999000}$ 22) $25,05(2589) = 25\frac{52589-5}{999900} = 25\frac{52584}{999900} = 25\frac{13146}{249975} = 25\frac{4382}{83325}$ 23) $9,0981(123) = 9\frac{0981123-0981}{9990000} = 9\frac{980142}{9990000} = 9\frac{490071}{4995000}$ 24) $0,000(001) = \frac{1}{999000}$ 5. Запишите в виде бесконечной периодической десятичной дроби: 1) $\frac{1}{3} = 0,(3)$ 2) $\frac{1}{9} = 0,(1)$ 3) $\frac{1}{11} = 0,(09)$ 4) $\frac{2}{7} = 0,(285714)$ 5) $\frac{7}{99} = 0,(07)$ 6) $\frac{5}{6} = 0,8(3)$ 7) $\frac{1}{14} = 0,0(714285)$ 8) $\frac{2}{15} = 0,1(3)$ 9) $2\frac{1}{12} = 2,08(3)$ 10) $4\frac{13}{24} = 4,541(6)$ 11) $4\frac{2}{45} = 4,0(4)$ 12) $\frac{12}{13} = 0,(923076)$ 13) $2\frac{5}{36} = 2,138(8)$ 14) $\frac{8}{11} = 0,(72)$ 15) $5\frac{5}{7} = 5,(714285)$ 16) $\frac{4}{33} = 0,(12)$ 17) $\frac{17}{28} = 0,6071428(571428)$ 18) $\frac{7}{85} = 0,082352941176470588235(...)$ 19) $1\frac{23}{48} = 1,47916(6)$ 20) $\frac{11}{18} = 0,61(1)$ 21) $\frac{43}{56} = 0,7678571428(571428)$ 22) $\frac{23}{30} = 0,76(6)$ 6. Вычислите удобным способом: 1) $41,(78)+34,(13)+17,(67) = (41 + \frac{78}{99}) + (34 + \frac{13}{99}) + (17 + \frac{67}{99}) = (41+34+17) + (\frac{78}{99} + \frac{13}{99} + \frac{67}{99}) = 92 + \frac{158}{99} = 92 + 1\frac{59}{99} = 93\frac{59}{99} = 93,(59)$ 2) $71,(059)+18,(215)+19,(125) = (71 + \frac{59}{999}) + (18 + \frac{215}{999}) + (19 + \frac{125}{999}) = (71+18+19) + (\frac{59}{999} + \frac{215}{999} + \frac{125}{999}) = 108 + \frac{399}{999} = 108 + \frac{133}{333} = 108,(133)$ 3) $\frac{20,(18)+14,(51)-12,(13)}{19,(51)+17,(18)-14,(13)}$ $20,(18) = 20 + \frac{18}{99}$ $14,(51) = 14 + \frac{51}{99}$ $12,(13) = 12 + \frac{13}{99}$ $19,(51) = 19 + \frac{51}{99}$ $17,(18) = 17 + \frac{18}{99}$ Числитель: $(20 + \frac{18}{99}) + (14 + \frac{51}{99}) - (12 + \frac{13}{99}) = (20+14-12) + (\frac{18}{99} + \frac{51}{99} - \frac{13}{99}) = 22 + \frac{56}{99}$ Знаменатель: $(19 + \frac{51}{99}) + (17 + \frac{18}{99}) - (14 + \frac{13}{99}) = (19+17-14) + (\frac{51}{99} + \frac{18}{99} - \frac{13}{99}) = 22 + \frac{56}{99}$ Значит, дробь равна $\frac{22 + \frac{56}{99}}{22 + \frac{56}{99}} = 1$ **Ответ:** 4. Представить в виде обыкновенной дроби: 1) $\frac{8}{9}$ 2) $\frac{233}{990}$ 3) $\frac{5}{9}$ 4) $\frac{36}{11}$ 5) $\frac{53}{90}$ 6) $28\frac{991}{9900}$ 7) $4\frac{431}{990}$ 8) $\frac{32}{75}$ 9) $\frac{25}{990}$ 10) $2\frac{313}{990}$ 11) $24\frac{53}{225}$ 12) $\frac{11}{45}$ 13) $167\frac{89}{99}$ 14) $1\frac{59}{495}$ 15) $25\frac{2}{11}$ 16) $1\frac{1008723}{990000}$ 17) $\frac{11561}{49950}$ 18) $2\frac{2113}{11000}$ 19) $10\frac{41}{45}$ 20) $1\frac{1}{111}$ 21) $9\frac{989011}{999000}$ 22) $25\frac{4382}{83325}$ 23) $9\frac{490071}{4995000}$ 24) $\frac{1}{999000}$ 5. Записать в виде бесконечной периодической десятичной дроби: 1) $0,(3)$ 2) $0,(1)$ 3) $0,(09)$ 4) $0,(285714)$ 5) $0,(07)$ 6) $0,8(3)$ 7) $0,0(714285)$ 8) $0,1(3)$ 9) $2,08(3)$ 10) $4,541(6)$ 11) $4,0(4)$ 12) $0,(923076)$ 13) $2,138(8)$ 14) $0,(72)$ 15) $5,(714285)$ 16) $0,(12)$ 17) $0,6071428(571428)$ 18) $0,082352941176470588235(..)$ 19) $1,47916(6)$ 20) $0,61(1)$ 21) $0,7678571428(571428)$ 22) $0,76(6)$ 6. Вычислить удобным способом: 1) $93,(59)$ 2) $108,(133)$ 3) $1$