Question

Transforme em fração irredutível cada dízima periódica: a)⇒0,151515...b)⇒0,287c)⇒0,444...d)⇒0,2414141...e)⇒0,3263f) ⇒0,185222...g)⇒1,111...h)⇒0,0111...i) ⇒2,1222...j) ⇒5,546

Answer 1

a)⇒0,151515...

15 / 99 ( ÷3)
5 / 33




b)⇒0,287

287 / 1000



c)⇒0,444...


4 / 9



d)⇒0,2414141...

x = 0,2414141... (×10)
10x = 2 + 41 / 99 (×99)
990x = 198 + 41
990x = 239
x = 239 / 990





e)⇒0,3263

3263 / 10000




f) ⇒0,185222...

x = 0,185222... (×1000)
1000x = 185 + 2 / 9 (×9)
9000x = 1665 + 2
9000x = 1667
x = 1667 / 9000



g)⇒1,111...

x = 1 + 1 / 9 (×9)
9x = 9 + 1
9x = 10
x = 10 / 9



h)⇒0,0111..


x = 0,0111... (×10
10x = 0 + 1/9 (×9)
90x = 0 + 1
x = 1 / 90



i) ⇒2,1222...

x = 2,1222... (×10
10x = 21 + 2/9 (×9
90x = 189 + 2
x = 191 / 90




j) ⇒5,546

5546 / 1000 (÷2)
2773 / 500