0.1 Recurring as a Fraction in Simplest Form
What is 0.1 Recurring?
0.1 recurring, also known as 0.1̄, is a decimal number that has a repeating pattern of 1s. It can be written as 0.11111... where the sequence of 1s goes on indefinitely. This type of decimal is known as a recurring decimal or a repeating decimal.
Converting 0.1 Recurring to a Fraction
To convert 0.1 recurring to a fraction, we need to find a way to express it as a ratio of two integers. One way to do this is to use the following method:
Let x = 0.1̄
Multiply both sides by 10 to get:
10x = 1.1̄
Subtract x from both sides to get:
9x = 1
Divide both sides by 9 to get:
x = 1/9
Therefore, 0.1 recurring can be written as a fraction in its simplest form as:
1/9
Why is 1/9 the Simplest Form?
To understand why 1/9 is the simplest form of 0.1 recurring, let's consider the following:
- The numerator (1) is the smallest possible integer that can be used to represent the decimal.
- The denominator (9) is the smallest possible integer that can be used to represent the repeating pattern of 1s.
- There is no other fraction with a smaller numerator and denominator that can represent 0.1 recurring exactly.
Therefore, 1/9 is the simplest form of 0.1 recurring.
Conclusion
In conclusion, 0.1 recurring can be written as a fraction in its simplest form as 1/9. This fraction represents the decimal 0.1 recurring exactly, with the smallest possible numerator and denominator.
