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...