2.6 Repeating as a Fraction
What is 2.6 Repeating?
2.6 repeating, also written as 2.6..., is a decimal number that has a repeating pattern of 6's after the decimal point. This means that the number 2.6 is followed by an infinite string of 6's.
Converting 2.6 Repeating to a Fraction
To convert 2.6 repeating to a fraction, we can use the following steps:
Step 1: Let's assume that the repeating decimal is x.
x = 2.6...
Step 2: Multiply both sides of the equation by 10 to shift the decimal point one place to the right.
10x = 26.6...
Step 3: Subtract the original equation from the new equation to eliminate the repeating decimal.
10x - x = 26.6... - 2.6...
This simplifies to:
9x = 24
Step 4: Divide both sides of the equation by 9 to solve for x.
x = 24/9
Step 5: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3.
x = 8/3
Therefore, 2.6 repeating can be written as a fraction in its simplest form as:
2.6... = 8/3
Conclusion
In conclusion, we have successfully converted the repeating decimal 2.6... to a fraction, which is equal to 8/3. This method can be applied to any repeating decimal to convert it into a fraction.
