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Find the exact value of 1.36666... .

Let x = 1.3666...

x = 1.3666... (multiply by 10 to both sides)

10x = 13.666... (subtract the first row from the second row)

9x = 12.3000... or

9x = 12.3 (multiply both sides by 10)

90x = 123 (divide both sides by 90)

x = 123/90 (divide the numerator and the denominator to obtain the simplest form of the fraction)

x = 41/30

Thus, 1.366666... = 41/30

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