Recurring Decimal 0.2 as a Fraction
What is a Recurring Decimal?
A recurring decimal, also known as a repeating decimal, is a decimal number that has a sequence of digits that repeats indefinitely in a predictable cycle. For example, the decimal 0.12341234... is a recurring decimal because the sequence "1234" repeats indefinitely.
The Recurring Decimal 0.2
The decimal 0.2 is a recurring decimal because it has a sequence of digits that repeats indefinitely. In this case, the sequence is simply "2" repeating indefinitely, making it a very simple recurring decimal.
Converting 0.2 to a Fraction
To convert the recurring decimal 0.2 to a fraction, we can use the following steps:
- Let x = 0.2
- Multiply both sides of the equation by 10 to get 10x = 2.0
- Subtract x from both sides of the equation to get 9x = 1.8
- Divide both sides of the equation by 9 to get x = 1/5
Therefore, the recurring decimal 0.2 is equal to the fraction 1/5.
Properties of the Fraction 1/5
The fraction 1/5 has several interesting properties:
- It is a unit fraction, meaning it has a numerator of 1.
- It is a common fraction, meaning it can be expressed as a finite decimal.
- It is an irreducible fraction, meaning it cannot be simplified further.
Conclusion
In conclusion, the recurring decimal 0.2 can be converted to the fraction 1/5 using simple arithmetic operations. This fraction has several interesting properties, including being a unit fraction, common fraction, and irreducible fraction.
