0.1 Recurring as a Fraction
Introduction
Recurring decimals, also known as repeating decimals, are a type of decimal number that has a sequence of digits that repeats indefinitely. One common example of a recurring decimal is 0.1, which can be written as 0.1111... where the sequence of 1's goes on forever. But have you ever wondered how to convert 0.1 recurring into a fraction? In this article, we'll explore how to do just that.
What is a Recurring Decimal?
Before we dive into converting 0.1 recurring into a fraction, let's take a quick look at what a recurring decimal is. A recurring decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.12345678901234567890... is a recurring decimal because the sequence of digits 123456789 repeats indefinitely.
Converting 0.1 Recurring to a Fraction
To convert 0.1 recurring into a fraction, we can use a simple technique. Let's say we have the equation:
x = 0.1111...
We can multiply both sides of the equation by 10 to get:
10x = 1.1111...
Now, subtract the original equation from the new equation:
10x - x = 1.1111... - 0.1111...
This simplifies to:
9x = 1
Dividing both sides by 9 gives us:
x = 1/9
So, 0.1 recurring is equal to 1/9.
Conclusion
In this article, we've seen how to convert 0.1 recurring into a fraction using a simple technique. This technique can be applied to any recurring decimal, making it a powerful tool for converting between different number systems. Whether you're working with decimals, fractions, or percentages, understanding how to convert between them is an important part of mathematics.
Key Takeaways
- 0.1 recurring is equal to 1/9
- Recurring decimals can be converted into fractions using a simple technique
- This technique can be applied to any recurring decimal
