0.167 Repeating as a Fraction
Introduction
Recurring decimals, also known as repeating decimals, are a type of decimal that has a sequence of digits that repeats indefinitely. One such example is 0.167 repeating. But have you ever wondered what this repeating decimal represents as a fraction? In this article, we will explore how to convert 0.167 repeating into its fractional equivalent.
Understanding Repeating Decimals
A repeating decimal is a decimal that has a sequence of digits that repeats in a predictable pattern. For example, 0.167 repeating can be written as 0.167167167..., where the sequence "167" repeats indefinitely. Repeating decimals can be converted into fractions, which are a more concise way of representing the same value.
Converting 0.167 Repeating into a Fraction
To convert 0.167 repeating into a fraction, we can use the following steps:
- Let x = 0.167167... We start by letting x equal the repeating decimal 0.167 repeating.
- Multiply both sides by 1000 To eliminate the fractional part, we multiply both sides of the equation by 1000, which results in:
1000x = 167.167... 3. Subtract the original equation from the new equation We subtract the original equation from the new equation to eliminate the fractional part:
1000x - x = 167.167... - 0.167...
This simplifies to:
999x = 167
Simplifying the Fraction
Now, we can simplify the fraction by dividing both sides of the equation by 999:
x = 167/999
Therefore, 0.167 repeating is equal to the fraction 167/999.
Conclusion
In conclusion, we have successfully converted 0.167 repeating into its fractional equivalent, which is 167/999. This process can be applied to any repeating decimal to find its corresponding fraction. Understanding how to convert between these two forms can help deepen our understanding of mathematics and improve our problem-solving skills.
