How do you convert 0.16 (6 repeating) to a fraction?
February 20th, 2023
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##
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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##