.66666 Repeating as a Fraction
Introduction
Have you ever wondered what the mysterious repeating decimal .66666 represents as a fraction? In this article, we'll explore the conversion of this repeating decimal to a simplified fraction.
Converting Repeating Decimals to Fractions
To convert a repeating decimal to a fraction, we can use a simple trick. Let's assume the repeating decimal is .66666. We can set up an equation by multiplying both sides by 10, since the repeating part is 6:
10x = 6.66666
Now, multiply both sides by 10 again to get:
100x = 66.6666
Subtract the first equation from the second equation:
90x = 60
Divide both sides by 90:
x = 60/90
Simplify the fraction:
x = 2/3
Result
The repeating decimal .66666 represents the fraction 2/3.
Conclusion
In conclusion, the mysterious repeating decimal .66666 is actually a simple fraction, 2/3. This conversion technique can be applied to any repeating decimal, providing a fascinating connection between the world of decimals and fractions.
