.6666 Repeating as a Fraction
The repeating decimal .6666... is a common mathematical concept that can be converted into a fraction. In this article, we will explore how to convert .6666... into a fraction and discuss its properties.
What is .6666...?
.6666... is a repeating decimal, where the sequence of digits "6" repeats indefinitely. This type of decimal is also known as a recurring decimal or a repeating decimal. Repeating decimals can be found in many mathematical concepts, including fractions, percentages, and ratios.
Converting .6666... to a Fraction
To convert .6666... to a fraction, we can use the following steps:
Step 1: Let x = .6666...
Let x be equal to .6666... This will be our starting point for converting the repeating decimal to a fraction.
Step 2: Multiply x by 10
Multiply x by 10 to get 10x = 6.6666... This will help us to isolate the repeating decimal.
Step 3: Subtract x from 10x
Subtract x from 10x to get 9x = 6. This will eliminate the repeating decimal and leave us with a simple equation.
Step 4: Solve for x
Solve for x by dividing both sides of the equation by 9. This will give us x = 2/3.
So, .6666... as a Fraction is 2/3
The repeating decimal .6666... can be converted into a fraction, which is 2/3. This fraction is a simple fraction, where the numerator is 2 and the denominator is 3.
Properties of 2/3
The fraction 2/3 has several interesting properties:
- Equivalent Ratios: 2/3 is equivalent to other ratios, such as 4/6, 6/9, and 8/12.
- Irreducible: 2/3 is an irreducible fraction, meaning it cannot be simplified further.
- Recurring Decimal: 2/3 can be converted back into a repeating decimal, which is .6666...
Conclusion
In conclusion, .6666... can be converted into a fraction, which is 2/3. This fraction has several interesting properties, including equivalent ratios, irreducibility, and the ability to be converted back into a repeating decimal. Understanding how to convert repeating decimals into fractions is an important concept in mathematics, and it has many practical applications in real-world problems.
