Resposta:

Explicação passo a passo:

a.

x=2,4545...

100x=245,4545...

100x-x=245,4545....-2,4545...

99x=243

x=243/99 [simplifica por 9]

x=27/11

b.

x=1,24444...

10x=12,4444...

100x=124,444....

100x-10x=124,4444...-12,444...

90x=112

x=112/90 [simplifica por 2]

x=56/45

c.

x=2,71111...

10x=27,1111...

100x=271,111...

100x-10x=271,111...-27,111...

90x=244

x=244/90 [simplifica por 2]

x=122/45

d.

x=0,262626...

100x=26,2626...

100x-x=26,2626...-0,2626..

99x=26

x=26/99