How do you convert -0.16 (6 being repeated) to a fraction?

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Answer 1 · 2016-08-02T11:25:17

#-13/18#

#color(red)("Note that this is a negative number")#

Write as #(-1) xx 0.16bar6#

Let #x=0.16bar6#

Then #10 x = 1.66bar6#

So #10x-x ->x(10-1) -> 9x= 1.66bar6#
#" "ul(0.16bar6) larr" Subtract"#

#9x=1.5#

Double both sides#" "18x=3#

Divide both sides by 18

#x=3/18#

But this now needs to be# (-1)xx3/18 = -3/18#