0.1 Recurring in Simplest Form
What is 0.1 Recurring?
0.1 recurring, also known as 0.1 repeating, is a decimal value that has an infinite number of repeating digits. It is a non-terminating decimal that has a sequence of digits that repeats indefinitely. In this case, the sequence is simply the digit 1.
Repeating Decimal Notation
In repeating decimal notation, 0.1 recurring is written as:
0.111111... (where the dots indicate that the sequence of 1s repeats indefinitely)
Simplest Form
To express 0.1 recurring in its simplest form, we can convert it to a fraction. To do this, we can use the following steps:
- Let x = 0.111111... (where x is the recurring decimal)
- Multiply both sides by 10 to get 10x = 1.111111...
- Subtract the original equation from the new equation to get 9x = 1
- Divide both sides by 9 to get x = 1/9
So, the simplest form of 0.1 recurring is:
1/9
Conclusion
In conclusion, 0.1 recurring is a non-terminating decimal that can be expressed in its simplest form as a fraction, which is 1/9. This equivalent fraction can be useful for various mathematical operations and calculations.
