0.7222 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal to a fraction? In this article, we will explore the process of converting 0.7222 repeating to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.7222, the sequence "22" repeats indefinitely.
Converting 0.7222 to a Fraction
To convert 0.7222 to a fraction, we can use the following steps:
Step 1: Let x = 0.7222
Let's start by letting x equal 0.7222.
Step 2: Multiply x by 100
Since the repeating sequence "22" has two digits, we multiply x by 100 to shift the decimal point two places to the right.
100x = 72.22
Step 3: Subtract x from 100x
Now, let's subtract x from 100x to eliminate the decimal part.
100x - x = 72.22 - 0.7222 99x = 71.50
Step 4: Simplify the Fraction
Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
x = 71.50 / 99 x = 7150 / 990 x = 715 / 99
So, 0.7222 repeating is equal to the fraction 715 / 99.
Conclusion
In this article, we learned how to convert the repeating decimal 0.7222 to a fraction using a simple and straightforward process. By following these steps, you can convert any repeating decimal to a fraction. Remember to always simplify your fraction by dividing both the numerator and the denominator by their GCD to get the simplest form.
