Odpowiedź :
Odpowiedź:
a) 0,(36)
x = 0,363636...
100x = 36,363636...
99x = 36
[tex]x = \frac{36}{99} = \frac{12}{33} = \frac{4}{11}[/tex]
[tex]0,(36) = \frac{4}{11}[/tex]
b) 0,(06)
x = 0,060606...
100x = 6,060606...
99x = 6
[tex]x = \frac{6}{99} = \frac{2}{33}[/tex]
[tex]0,(06) =\frac{2}{33}[/tex]
c) 3,(72)
x = 3,727272...
100x = 372,727272..
99x = 369
[tex]x = \frac{369}{99} = \frac{41}{11}[/tex]
[tex]3,(72) = \frac{41}{11}[/tex]
d) - 6,(24)
x = - 6,242424...
100x = - 624,242424...
99x = - 618
[tex]x = -\frac{618}{99} =- \frac{206}{33}[/tex]
[tex]-6,(24) = -\frac{206}{33}[/tex]
e) 0,(9)
x = 0,999...
10x = 9,999...
9x = 9
[tex]x = \frac{9}{9}[/tex]
[tex]0,(9) = \frac{9}{9}[/tex]
f) 41,7(9)
x = 41,7999...
10x = 417,999...
100x = 4179,999.
90x = 3762
[tex]x = \frac{3762}{90} = \frac{209}{5}[/tex]
g) 0,(369)
x = 0,369369369...
1000x = 369,369369369...
999x = 369
[tex]x =\frac{369}{999} = \frac{41}{111}[/tex]
[tex]0,(369) = \frac{41}{111}[/tex]
h) 2,1(52)
x = 2,1525252...
10x = 21,525252...
1000x = 2152,525252...
990x = 2131
[tex]x = \frac{2131}{990}[/tex]
[tex]2,1(52) = \frac{2131}{990}[/tex]