16666 Repeating as a Fraction
The repeating decimal 0.16666... is a fascinating mathematical entity that has sparked curiosity among math enthusiasts. In this article, we will explore how to convert this repeating decimal into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.16666..., the sequence "66" repeats indefinitely. Repeating decimals can be converted into fractions, which can be a more convenient and intuitive way to represent these numbers.
Converting 0.16666... to a Fraction
To convert 0.16666... to a fraction, we can use the following steps:
Step 1: Let x = 0.16666...
Let's start by letting x be equal to 0.16666.... This will help us to manipulate the equation and arrive at a solution.
Step 2: Multiply x by 100
Next, we multiply x by 100, which gives us:
100x = 16.666...
Step 3: Subtract x from 100x
Now, we subtract x from 100x, which gives us:
99x = 16.5
Step 4: Solve for x
Finally, we can solve for x by dividing both sides of the equation by 99:
x = 16.5/99
x = 1/6
So, the repeating decimal 0.16666... is equal to the fraction 1/6.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.16666... into the fraction 1/6. This demonstrates the power of mathematical manipulation and the importance of understanding the properties of repeating decimals. Whether you're a math enthusiast or just looking to improve your problem-solving skills, converting repeating decimals to fractions is a valuable tool to have in your mathematical toolkit.
