How do you convert 0.16 (6 repeating) to a fraction?

A ##underline("very slightly")## different way of writing the solution

##1.6bar6" "->" " 1/6##

Note: if the 6 is repeating then a way of showing this is to put a bar over the last 6 you write: ##->" "0.16bar6## '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Let ##x=0.16bar6##

Then ##10x=1.6bar6## Also ##100x=16.6bar6##

##100x-10x->" "16.6bar6## ##" "underline(" "1.6bar6)" Subtract"## ##" "underline(" "15" ")" "##

So ##90x =15##

Divide both sides by 90 ##" "x=15/90##

But ##15/90->(15-:15)/(90-:15) = 1/6##

##=>x=1.6bar6" "->" " 1/6##