The decimal 2.66666 (often written as 2.6666โฆ) appears in math, finance, averages, and ratios. Because the digit 6 repeats, this number is not a terminating decimal โ it is a repeating decimal.
That changes the conversion method slightly compared to decimals like 1.25 or 2.5.
So the key question is:
What is 2.66666 as a fraction?
Letโs convert it step by step, simplify it correctly, verify the result, and understand where this fraction is commonly used.
Why Convert 2.66666 Into a Fraction?
Converting repeating decimals into fractions is important when:
- Solving algebra and ratio problems
- Avoiding rounding errors
- Working with exact values instead of approximations
- Using fractions in equations and proofs
- Preparing for exams and competitive tests
Fractions give an exact value, while decimals like 2.66666 are often rounded in practice.
Understanding the Decimal 2.66666
The number 2.66666โฆ means:
- The digit 6 repeats forever
- It is written mathematically as 2.6ฬ
- It is a rational number, because it can be expressed as a fraction
Step 1: Separate the Whole Number
Start by separating the whole number from the decimal part:
2.66666โฆ = 2 + 0.66666โฆ
Now we only need to convert 0.66666โฆ into a fraction.
Step 2: Convert 0.66666โฆ Into a Fraction
A well-known repeating decimal rule:
0.66666โฆ = 2 / 3
(This is because 2 รท 3 = 0.66666โฆ)
Step 3: Add the Whole Number Back
Now add the whole number part:
2 + 2/3
Convert 2 into thirds:
2 = 6/3
So:
6/3 + 2/3 = 8/3
โ Final Simplified Fraction
2.66666โฆ as a fraction = 8 / 3
Optional: Write as a Mixed Number
Because 8/3 is an improper fraction, it can also be written as a mixed number:
8/3 = 2 2/3
Both forms are correct:
- 8/3 (preferred in math)
- 2 2/3 (preferred in everyday use)
Step 4: Verify the Answer
Decimal Check
Divide the numerator by the denominator:
8 รท 3 = 2.66666โฆ
โ Correct
Fraction Breakdown Check
2 2/3 = 2 + 2/3 = 2.66666โฆ
โ Verified
Is 8/3 an Improper Fraction?
Yes.
The numerator (8) is greater than the denominator (3), so 8/3 is an improper fraction.
Thatโs why it can also be written as 2 2/3.
Real-Life Examples of 2.66666 as a Fraction
โฑ Time
- 2.66666 hours = 2 2/3 hours
- Equals 2 hours 40 minutes
- Common in scheduling and work logs
๐ Measurements
- 2.66666 meters = 2 2/3 meters
- Used in construction and design calculations
๐งฎ Mathematics & Ratios
- Appears in averages and division problems
- Easier to work with as 8/3 in equations
๐ Finance & Statistics
- Average values like 8 รท 3
- Avoids rounding errors compared to decimals
Common Mistakes to Avoid
- โ Rounding 2.66666 to 2.67 (loses accuracy)
- โ Writing 2.66666 as 266666/100000 (incorrect)
- โ Forgetting that the 6 repeats
- โ Leaving the answer as a long decimal instead of a fraction
Always check whether the decimal repeats or terminates.
FAQs: 2.66666 as a Fraction
What is 2.66666 as a fraction in simplest form?
8/3
Is 2.66666 a repeating decimal?
Yes. The digit 6 repeats indefinitely.
Is 2.66666 a rational number?
Yes. All repeating decimals are rational numbers.
Can 2.66666 be written as a mixed number?
Yes. 2 2/3
Why does 0.66666 equal 2/3?
Because dividing 2 by 3 produces a repeating decimal: 0.66666โฆ
โ Final Answer Box
What Is 2.66666 as a Fraction?
8/3 or 2 2/3
Key Takeaway
To convert 2.66666 into a fraction:
- Recognize it as a repeating decimal
- Separate the whole number (2)
- Convert 0.66666โฆ โ 2/3
- Add them together โ 8/3
- Write as 2 2/3 if needed
This approach ensures exact results, making it essential for math, finance, science, and exam preparation.
