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 is $$0.66667
Step 3:: Convert to a fraction
Let $$x = 0.66667
To convert a repeating decimal to a fraction, we'll use algebraic manipulation:
Step 4:: Set up the equation
1000x = 666.67
x = 0.66667
Step 5:: Subtract to eliminate decimals
999x = 666
x = 0.66667
Step 6:: Solve for the fraction
x = \frac{666}{999}
Step 7:: Simplify the fraction
\frac{666}{999} = \frac{2}{3}$$ (by dividing both numerator and denominator by 333)
Final Answer
\frac{2}{3}
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