Overline 6 as a Fraction
In mathematics, an overline is a symbol used to indicate that a digit or a group of digits in a number should be repeated indefinitely. In this article, we will explore the concept of overline 6 as a fraction.
What is Overline 6?
The overline 6 is a symbol that represents the repeating decimal 0.666... The dots indicate that the sequence of 6s goes on indefinitely. This notation is often used to simplify the representation of repeating decimals.
Converting Overline 6 to a Fraction
To convert the overline 6 to a fraction, we can use the following steps:
Step 1: Let the Overline 6 be Equal to x
Let the overline 6 be equal to x. This means that x = 0.666...
Step 2: Multiply Both Sides by 10
Multiply both sides of the equation by 10 to get:
10x = 6.666...
Step 3: Subtract the Original Equation from the New Equation
Subtract the original equation from the new equation to get:
9x = 6
Step 4: Solve for x
Divide both sides of the equation by 9 to solve for x:
x = 6/9
Step 5: Simplify the Fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
x = 2/3
Therefore, the overline 6 as a fraction is 2/3.
Conclusion
In conclusion, the overline 6 can be converted to a fraction by following the steps outlined above. The resulting fraction is 2/3, which is a simplified representation of the repeating decimal 0.666... Understanding how to convert overlines to fractions is an important concept in mathematics, as it helps to simplify complex numerical representations.
