.38888 Repeating as a Fraction
The repeating decimal .38888 is a fascinating mathematical phenomenon that can be converted into a fraction. In this article, we will explore how to convert .38888 into a fraction and delve into its properties.
Converting .38888 to a Fraction
To convert the repeating decimal .38888 into a fraction, we can use the following steps:
- Let x = .38888
- Multiply both sides by 100, since the repeating part is 2 digits long:
100x = 38.888 3. Subtract x from both sides to eliminate the repeating part:
100x - x = 38.888 - .38888 99x = 38.5 4. Divide both sides by 99:
x = 38.5 / 99 x = 388 / 990
So, .38888 repeating as a fraction is equal to 388 / 990, which can be simplified to 97 / 247.5.
Properties of .38888 as a Fraction
Now that we have converted .38888 into a fraction, let's explore some of its properties:
- Simplification: As mentioned earlier, the fraction can be simplified to 97 / 247.5.
- Reduced Form: The fraction in its reduced form is 194 / 495.
- Decimal Equivalent: The decimal equivalent of the fraction is, of course, .38888.
- Repeating Pattern: The repeating pattern of .38888 is infinite, meaning it goes on indefinitely.
Conclusion
In conclusion, .38888 repeating can be converted into a fraction, specifically 388 / 990, which can be simplified to 97 / 247.5. Understanding the properties of this fraction, such as its simplification, reduced form, decimal equivalent, and repeating pattern, can help deepen our appreciation for the mathematical concept of repeating decimals.
