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Ответ:

Пошаговое объяснение:

1. 0,(8)=8/9; 1,(7)=1⁷/₉; 10,(45)=10⁴⁵/₉₉=10⁵/₁₁; 0,1(6)=15/90; 8,7(5)=8⁶⁸/₉₀; 15,1(34)=15¹³³/₉₉₀.

2.

10x-x=4,333...-0,4333..

9x=4,(3)-0,4(3)

9x=4¹/₃-³⁹/₉₀

9x=(13/3)-(13/30)

9x=(13*10-13)/30  |÷9

x=117/270

x=13/30.

3.

a) 0,(2)=2/9; 1,(3)=1¹/₃; 3,(54)=3⁶/₁₁; 21,(23)=21²³/₉₉; 0,(673)=663/999;

7,(256)=7²⁵⁶/₉₉₉; 16,(002)=16²/₉₉₉; 0,(0001)=1/9999; 5,(01)=5¹/₉₉.

б) 0,1(3)=12/90; 1,2(5)=1²³/₉₀; 7,0(4)=7²/₄₅; 2,23(7)=2¹⁰⁷/₄₅₀;

10,1(45)=10⁸/₅₅; 0,25(83)=1279/4950; 16,5(02)=16⁴⁹⁷/₉₉₀;

0,000(1)=1/9000.