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The fraction that equals 0.2666666666666667 is 4/15. To convert the repeating decimal 0.2666666666666667 to a fraction, we can write it as x = 0.26 + 0.0066 + 0.000066 + ... and solve for x. This can be simplified to x = 26/100 + 6/900 + 6/90000 + ... = 26/100 + 6/900(1 + 1/100 + 1/10000 + ...) = 26/100 + 6/900(1/(1-1/100)) = 26/100 + 6/900(100/99) = 26/100 + 6/15 = 4/15.
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