Question

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

Answer 1

a)⇒0,151515...   = 15/99
b)⇒0,287     
c)⇒0,444...         = 4/9
d)⇒0,2414141...  

$0,2414141..=\frac{2,414141..}{10}=\frac{2+\frac{41}{99}}{10}=\frac{239}{990}$

e)⇒0,3263
f) ⇒0,185222...
$0,185222...=\frac{185,2222..}{1000}=\frac{185+\frac{2}{9}}{1000}=\frac{1667}{9000}$

g)⇒1,111... = 1+ 1/9 = 10/9

h)⇒0,0111...

$0,0111...=\frac{0,1111..}{10}=\frac{\frac{1}{9}}{10}=\frac{1}{90}$

i) ⇒2,1222...

$2,1222... = \frac{21,222...}{10}=\frac{21+\frac{2}{9}}{10}=\frac{191}{90}$
j) ⇒5,546