Rozwiązane

Przedstaw liczbę w postaci ułamka zwykłego. a) 0,(36) b) 0,(06) c) 3,(72) d) -6(24) e) 0,(9) f) 41,7(9) g) 0,(369) h) 2,1(52) PROSZĘ O ROZWIĄZANIA WRAZ Z RACHUNKAMI!



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]

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