To express the decimal 0.66666666667 as a fraction, we can recognize that this decimal is a repeating decimal, often represented simply as 0.666… (where the 6 repeats indefinitely).
1. **Recognize the repeating part:** The number can be rewritten as 0.666… . This means that there are infinitely many 6’s following the decimal point.
2. **Set up an equation:** Let x = 0.666…. Multiplying both sides of this equation by 10 gives us:
10x = 6.666…
3. **Subtract the original equation from this new equation:**
10x – x = 6.666… – 0.666…
This simplifies to:
9x = 6
4. **Solve for x:** Now, divide both sides by 9:
x = 6/9
5. **Simplify the fraction:** The fraction 6/9 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
6 ÷ 3 = 2 and 9 ÷ 3 = 3, giving us:
x = 2/3
Thus, the decimal 0.66666666667 expressed as a fraction is 2/3.