0.1 Recurring as a Fraction
In mathematics, a recurring decimal is a decimal that has a infinite sequence of repeating digits. One common example of a recurring decimal is 0.1 recurring, also known as 0.111... (where the dots represent the infinite repetition of the digit 1).
What is 0.1 Recurring?
0.1 recurring is a decimal number that has an infinite sequence of repeating 1s. It can be written as:
0.1, 0.11, 0.111, 0.1111, ... (and so on)
The decimal never ends, and the digit 1 is repeated indefinitely.
Converting 0.1 Recurring to a Fraction
To convert 0.1 recurring to a fraction, we can use a simple method. Let's assume that:
x = 0.111... (where x is the decimal number)
We can multiply both sides of the equation by 10 to get:
10x = 1.111...
Now, subtract x from both sides to get:
9x = 1
x = 1/9
So, 0.1 recurring is equal to the fraction 1/9.
Understanding the Fraction
The fraction 1/9 is a simple fraction that can be simplified no further. It is an equivalent ratio of one part out of nine equal parts.
Real-World Applications
Recurring decimals like 0.1 recurring have many real-world applications, such as:
- Finance: Recurring decimals are used in financial calculations, such as interest rates and investment returns.
- Science: Recurring decimals are used in scientific calculations, such as measurements and conversions.
- Engineering: Recurring decimals are used in engineering calculations, such as stress and strain calculations.
Conclusion
In conclusion, 0.1 recurring is a decimal number that has an infinite sequence of repeating 1s. It can be converted to a fraction, which is equal to 1/9. Understanding recurring decimals and their equivalent fractions is an important part of mathematics, and has many practical applications in various fields.
