Question

Transforme em fração irredutível cada dízima periódica:Transforme em fração irredutível cada dízima periódica:  MIM AJUDEMa)⇒0,151515...b)⇒0,287c)⇒0,777...d)⇒0,2414141...e)⇒0,3263f) ⇒0,185222...g)⇒1,111...h)⇒0,0111...i) ⇒2,1222...j) ⇒5,546

Answer 1

Considere que x seja a fração de de cada dízima.

a)$x = 0,151515...$
$100x = 15,151515...$
$100x - x = 15,151515... - 0,151515... = 15$
$99x = 15$
$x = 15/99 = 5/33$
b)$x = 0,287287...$
$1000x = 287,287287...$
$1000x - x = 287,287287... - 0,287287...$
$999x = 287$
$x = 287/999$
c)$x = 0,777...$
$10x - x = 7,777... - 0,777... = 7$
$9x = 7$
$x = 7/9$
d)$x = 0,2414141...$
$100x = 24,141414...$
$10000x = 2414,141414...$
$10000x - 100x = 2414,141414... - 24,141414... = 2390$
$9900x = 2390$
$x = 239/990$
e)$1000x = 362,362362362...$
$999x = 362,362362362... - 0,362362362... = 362$
$x = 362/999 =$
f)$1000x = 185,222...$
$10000x = 1852,222...$
$10000x - 1000x = 1852,222... - 185,222... = 1667$
$9900x = 1667$
$x = 1667/9900$
g)$10x - x= 11,111... - 1,111 = 10$
$9x = 10$
$x = 10/9$
h)$10x - x = 0,1111... - 0,0111... = 0,1$
$9x = 0,1 = 1/10$$x = 1/90$
i)$100x - x = 212,222... - 21,222... = 191$
$99x = 191$
$x = 191/99$
j)$1000x - x = 5546,546546546... - 5,546546546... = 5541$
$999x = 5541$
$x = 5541/999 = 1847/333$.