Question

Help with this question of grade 9 chapter 1

Answer 1

`0.6=(6)/(10)=(3)/(5)\\\\x=0.\overline{7}\\10x=7.\overline{7}\\10x-x=7.\overline{7}-0.\overline{7}\\9x=7\\x=(7)/(9)\\\\x=0.4\overline{7}\\10x=4.\overline{7}\\100x=47.\overline{7}\\100x-10x=47.\overline{7}-4.\overline{7}\\90x=43\\x=(43)/(90)`

Therefore

`0.6+0.\overline{7}+0.4\overline{7}=(3)/(5)+(7)/(9)+(43)/(90)=(54)/(90)+(70)/(90)+(43)/(90)=(167)/(90)`