How do you convert 0.26 (6 repeating) to a fraction?

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Answer 1 · 2016-02-28T03:34:33

#a/b=4/15" " "#the required fraction

Let #a/b# the unknown fraction

then #a/b=0.266666666....# call this the 1st equation

Multiply both sides of the equation by 10 to produce

#10a/b=2.66666666.....#call this the 2nd equation

Go back to the 1st equation and this time multiply both sides by 100 to obtain

#100a/b=26.66666666....#call this the 3rd equation

Now #color(blue)"subtract the 2nd from the 3rd"#

#100a/b-10a/b=26.66666666-2.66666666#

and we have

#90a/b=24#

solve for a/b

#a/b=24/90=4/15#

#a/b=4/15#

God bless...I hope the explanation is useful...