.6666 as a Fraction
The recurring decimal .6666 is a familiar sight to many of us. It's a decimal representation of a fraction, but what exactly is that fraction?
What is .6666 as a Fraction?
The decimal .6666 is equivalent to the fraction 2/3. Yes, you read that right! The repeating decimal .6666 can be expressed as a simple fraction, 2 divided by 3.
How to Convert .6666 to a Fraction
To convert the decimal .6666 to a fraction, we can use the following steps:
- ** Divide by the number of decimal places**: Since .6666 has 4 decimal places, we can divide it by 10,000 (10 to the power of 4).
.6666 ÷ 10,000 = 6666/10,000
- Simplify the fraction: We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 6666 and 10,000 is 2.
6666 ÷ 2 = 3333 10,000 ÷ 2 = 5000
So, the simplified fraction is:
3333/5000
- Find the equivalent fraction: Now, we can find the equivalent fraction by dividing both the numerator and the denominator by their GCD again.
The GCD of 3333 and 5000 is 333.
3333 ÷ 333 = 10 5000 ÷ 333 = 15
Therefore, the equivalent fraction is:
10/15
- Simplify the fraction further: We can simplify the fraction 10/15 by dividing both the numerator and the denominator by their GCD.
The GCD of 10 and 15 is 5.
10 ÷ 5 = 2 15 ÷ 5 = 3
And finally, we get:
2/3
Conclusion
The decimal .6666 is equivalent to the fraction 2/3. By following the steps outlined above, we can convert any recurring decimal to a fraction. This is a fundamental concept in mathematics, and understanding it can help us better grasp many mathematical concepts.
