2.66667 as a fraction

Daniel Parker

2 min read

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28-02-2025

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The decimal 2.66667 presents a slight challenge in conversion to a fraction because of the final digit 7. This suggests a rounding of a repeating decimal. Let's explore how to approach this, looking at both the exact value if we assume rounding and the process for dealing with repeating decimals if the '.66667' was actually a repeating '.666...'

Understanding Repeating Decimals

Before tackling 2.66667 specifically, let's review the general approach for converting repeating decimals to fractions. A repeating decimal like 0.666... (often written as 0.6̅) represents a fraction. Here's the method:

1. Assign a variable: Let x = 0.666...

2. Multiply to shift the decimal: Multiply both sides by 10 (or 100, 1000 etc. depending on the repeating pattern length): 10x = 6.666...

3. Subtract the original equation: Subtract the original equation (x = 0.666...) from the multiplied equation (10x = 6.666...). This eliminates the repeating part:

   10x - x = 6.666... - 0.666... 9x = 6

4. Solve for x: Divide both sides by 9 to isolate x:

   x = 6/9 = 2/3

Therefore, 0.666... is equivalent to 2/3.

Approximating 2.66667 as a Fraction

Since 2.66667 likely represents a rounded value, let's treat it as an approximation of 2.666... which we know is close to 2 and 2/3.

We can express this as:

2 + 2/3 = (6/3) + (2/3) = 8/3

Therefore, a close fractional approximation for 2.66667 is 8/3.

To get a more precise fraction, we can use the following method:

1. Separate the whole number: The whole number part is 2.

2. Focus on the decimal part: The decimal part is 0.66667.

3. Express as a fraction (approximate): Since 0.66667 is approximately 2/3 (from above), we can add this to the whole number.

4. Final approximation: This gives us 2 + 2/3 = 8/3

Finding the Exact Fraction (If Not Rounded)

If 2.66667 was not a rounded number, and the digits continued to repeat, we would treat it differently. However, without further clarification on whether the decimal repeats, we are working with an approximation.

Conclusion

While a perfectly repeating decimal like 2.666... translates cleanly to 8/3, the given decimal 2.66667 is most accurately represented by the fraction 8/3 as a very close approximation. Remember to consider the context of the number, as the final '7' suggests some rounding has occurred.