0.5244 Repeating as a Fraction
When dealing with repeating decimals, it's often more informative and useful to convert them into fractions. In this article, we'll explore how to convert the repeating decimal 0.5244 into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.5244, the sequence "5244" repeats indefinitely.
Converting 0.5244 to a Fraction
To convert 0.5244 into a fraction, we can use the following steps:
Step 1: Let x = 0.5244
Let's start by letting x equal 0.5244.
Step 2: Multiply x by 10,000
Next, we multiply x by 10,000 to get:
10,000x = 5,244.5244
Step 3: Subtract x from 10,000x
Now, we subtract x from 10,000x to get:
9,999x = 5,244
Step 4: Divide by 9,999
Finally, we divide both sides by 9,999 to get:
x = 5244/9999
Simplifying the Fraction
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9. This gives us:
x = 5816/1111
And that's it! We've successfully converted the repeating decimal 0.5244 into a fraction: 5816/1111.
Conclusion
Converting repeating decimals into fractions can be a useful skill in various mathematical and real-world applications. By following the steps outlined above, you can convert any repeating decimal into a fraction. Remember, practice makes perfect, so be sure to try converting different repeating decimals into fractions to become more comfortable with the process.
