Simplifying the Decimal .6667 to a Fraction
The decimal .6667 is a recurring decimal that can be simplified to a fraction. In this article, we will explore how to simplify .6667 to a fraction and understand its equivalent ratio.
Converting .6667 to a Fraction
To convert .6667 to a fraction, we can use the following steps:
- Write the decimal as a fraction with a denominator of 10: .6667 = 6667/10000
- Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD): The GCD of 6667 and 10000 is 1, so we cannot simplify the fraction further.
However, we can notice that .6667 is a repeating decimal, where the sequence "6" repeats indefinitely. This suggests that we can simplify the fraction further by using a different approach.
Using the Repeating Decimal Pattern
Since .6667 is a repeating decimal, we can set up an equation using the following pattern:
Let x = .6667
Multiply both sides by 10 to get:
10x = 6.667
Subtract x from both sides to get:
9x = 6
Divide both sides by 9 to get:
x = 6/9
Simplifying the Fraction
We can simplify the fraction 6/9 by dividing both the numerator and denominator by their GCD, which is 3:
6 ÷ 3 = 2 9 ÷ 3 = 3
So, the simplified fraction is:
.6667 = 2/3
Conclusion
In conclusion, the decimal .6667 can be simplified to the fraction 2/3. This equivalent ratio represents the same value as the recurring decimal .6667. By using the repeating decimal pattern and simplifying the fraction, we can express .6667 in a more concise and meaningful way.
