Question

Escreva sob forma de fração irredutível as seguintes dizimas periódicas:
a) 0, 235555... b) 0, 1333... c) 0, 1333... d) 5, 413333... e) 0, 344848...

Answer 1

a)x= 0,23555... (*100)
100x= 23,555...( *10)
1000x= 235,555...

1000x= 235,555...
-
100x= 23,555...

900x= 235 - 23
900x= 212

x= 212/ 900 (simplificando por 4)
x= 53/ 225 (resposta)

b) x= 0,1333... (*10)
10x= 1,333... (*10)
100x= 13,333...

100x= 13,333...
-
10x= 1,333...

90x= 13 -1
90x= 12

x= 12/90 ( simplificando por 6)
x= 2/15 ( resposta)

c) igual a letra b)

d) x= 5 + 0,41333...
x'= 0,41333... (*100)
100x'= 41,333... (*10)
1000x'= 413,333...

1000x' - 100x' = 413,333... - 41,333...
900x'= 372
x'= 372/900

x= 372/900 +5
x= 4872/ 900 (simplificando por 12)
x= 406/ 75( resposta)

e) x= 0,344848... (*100)
100x=34,4848.. ( *100)
10000x= 3448, 4848...

10000x- 100x= 3448,4848... - 34,4848...
9900x= 3414
x= 3414/9900 ( simplificando por 6)
x=569/ 1650 ( resposta)