Resposta :
Chamemos essa dízima periódica de d.
[tex]d=17.888 \, \dots\\[/tex]
Temos portanto que:
[tex]10 d = 178.888 \, \dots\\[/tex]
Logo:
[tex]10d -d = (178.888 \dots) - (17.888 \dots)\\9d=161\\\\\\d = 161/9[/tex]
Chamemos essa dízima periódica de d.
[tex]d=17.888 \, \dots\\[/tex]
Temos portanto que:
[tex]10 d = 178.888 \, \dots\\[/tex]
Logo:
[tex]10d -d = (178.888 \dots) - (17.888 \dots)\\9d=161\\\\\\d = 161/9[/tex]