The decimal 0.6667 is a recurring decimal, meaning it continues infinitely with the same pattern of digits. It's important to understand how to convert recurring decimals to fractions. Here's a breakdown:
Understanding the Recurring Decimal
The decimal 0.6667 represents a value that is slightly less than two-thirds (2/3). This is because the decimal portion goes on indefinitely, making it an approximation of the exact value.
Converting to a Fraction
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Set up an equation: Let 'x' equal the decimal: x = 0.6667
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Multiply to shift the decimal: Multiply both sides of the equation by 10,000 to move the decimal point four places to the right: 10,000x = 6667
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Subtract the original equation: Subtract the first equation (x = 0.6667) from the second equation (10,000x = 6667): 10,000x - x = 6667 - 0.6667 9,999x = 6666.3333
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Solve for x: Divide both sides by 9,999: x = 6666.3333 / 9999
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Simplify: Since the decimal part is still repeating, we need to simplify. Notice that both the numerator and denominator can be divided by 3333: x = 2 / 3
Conclusion
Therefore, the decimal 0.6667, when converted to a fraction, is approximately 2/3. It's crucial to understand the concept of recurring decimals and how to convert them into fractions to achieve accurate representations of these values.
