Answer
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Step 1:I'll solve this step-by-step using precise LaTeX formatting:
Step 2:: Identify the Decimal
The decimal number is $$0.6667
Step 3:: Convert to Fraction
Let $$x = 0.6667
To convert a repeating decimal to a fraction, we'll use the algebraic method:
Step 4:: Set Up Equation
10x = 6.6667
Multiply both sides by 10 to shift the decimal:
Step 5:: Subtract Original Equation
9x = 6
x = 0.6667
Step 6:: Solve for x
x = \frac{6}{9}
Step 7:: Simplify the Fraction
\frac{6}{9} = \frac{2}{3}$$ (divide both numerator and denominator by their greatest common factor of 3)
Final Answer
\frac{2}{3}
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