0.318 Repeating as a Fraction
The decimal number 0.318 repeating is a non-terminating and non-repeating decimal expansion. However, it can be expressed as a fraction. In this article, we will discuss how to convert 0.318 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely in a predictable pattern. For example, 0.318 repeating is a repeating decimal because the sequence of digits "318" repeats indefinitely.
Converting 0.318 Repeating into a Fraction
To convert 0.318 repeating into a fraction, we can use the following steps:
- Let x = 0.318 repeating
- Multiply both sides of the equation by 1000 to get 1000x = 318.318 repeating
- Subtract x from both sides of the equation to get 999x = 318
- Divide both sides of the equation by 999 to get x = 318/999
Simplifying the Fraction
The fraction 318/999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 318 and 999 is 3. Therefore, we can divide both the numerator and the denominator by 3 to get:
x = 318/999 = 106/333
Conclusion
In conclusion, the repeating decimal 0.318 repeating can be expressed as a fraction, which is 106/333. This fraction can be used in mathematical calculations and operations, making it easier to work with the decimal number.
Final Answer
0.318 repeating as a fraction is 106/333.
