2.6 Repeating as a Fraction
Sometimes, we come across numbers that seem to go on forever, repeating in a cycle. These numbers are known as repeating decimals, and they can be converted into fractions. One such example is 2.6 repeating.
What is 2.6 Repeating?
2.6 repeating, also written as 2.6..., is a decimal number that has a repeating pattern of 6 after the decimal point. This means that the number 2 is followed by an infinite string of 6s, like this: 2.666666... . As the sequence goes on forever, we can't write it out in full, but we can represent it using an ellipsis (...) to indicate the repeating pattern.
Converting 2.6 Repeating to a Fraction
To convert 2.6 repeating to a fraction, we can use a simple trick. We'll let x equal 2.6..., and then multiply both sides of the equation by 10 to get 10x = 26.6... .
Next, we'll subtract x from both sides to eliminate the repeating decimal part:
10x = 26.6... x = 2.6...
Subtracting x from both sides gives us:
9x = 24
Now, we can divide both sides by 9 to solve for x:
x = 24/9 x = 8/3
So, 2.6 repeating as a fraction is 8/3.
Why Does This Work?
This method works because multiplying by 10 essentially "shifts" the decimal point one place to the right, allowing us to eliminate the repeating part. By subtracting x from both sides, we're left with a simple equation that can be solved to find the fraction equivalent.
Conclusion
In conclusion, 2.6 repeating as a fraction is equal to 8/3. This conversion is possible using a simple trick involving multiplication and subtraction. By recognizing the pattern of the repeating decimal, we can convert it into a more familiar and workable fraction.
