Question

Escreva sob forma de fração irredutível as seguintes dízimas periódicas :
a) 0,5444...
b) 0,0505...
c) 0,3737...

Answer 1

a-0,5444...
x=0,5444..
10x=5,444..
100x=54,444
100x-10x=54,444-5,444
90x=49
x=49/90

b-0,0505...
x=0,0505...
1000x=50,505050...
100000x=5050,5050...
100000x-1000x=5050,5050-50,5050
99000x=5000
x=5000/99000
x=5/99

c-0,3737...

x=0,3737...
100x=37,3737...
10000x=3737,3737...
10000x-100x=3737,3737...-37,3737...
9900x=3700
x=3700/9900
x=37/99