.667 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal like .667 into a fraction? In this article, we'll explore how to do just that.
What is .667 Repeating?
.667 repeating is a decimal that never terminates and has a recurring pattern of 6, 6, and 7. It is often written as .667... with the ellipsis indicating that the pattern continues indefinitely.
Converting .667 Repeating to a Fraction
To convert .667 repeating to a fraction, we can use a simple trick. Let's multiply .667 by 1,000 to get:
667.667...
Now, subtract the original number from this new value:
667.667 - .667 = 667
This gives us:
667 = 999 * .667
Now, divide both sides by 999:
.667 = 667/999
Simplifying the Fraction
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 667 and 999 is 333, so we can divide both numbers by 333:
.667 = (667 ÷ 333) / (999 ÷ 333) .667 = 2/3
Final Answer
Therefore, .667 repeating is equal to the fraction 2/3.
Conclusion
Converting a repeating decimal like .667 to a fraction is a straightforward process. By using multiplication and subtraction, we can convert the decimal to a fraction, and then simplify it to its simplest form. In this case, .667 repeating is equal to the simple fraction 2/3.
