x=0.1515151515 2 places rpeat multily both sides by 100 100x=15.1515151515 minus x from both sides 100x-x=15.151515151515-0.1515151515 the repeating parts cancel and we get 99x=15 divide both sides by 99 [tex]x=\frac{15}{99}[/tex] [tex]x=\frac{5}{33}[/tex] x=0.151515
so therefor [tex]0.\overline{15}=\frac{5}{33}[/tex]
