0.1222 Repeating as a Fraction
The decimal 0.1222 repeating is a fascinating number that has a simple fraction equivalent. In this article, we will explore how to convert 0.1222 repeating into a fraction and understand the concept behind it.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.1222 repeating, the sequence "22" repeats indefinitely. This type of decimal is also known as a periodic decimal.
Converting 0.1222 Repeating to a Fraction
To convert 0.1222 repeating to a fraction, we can use the following method:
Let x = 0.1222...
Multiplying both sides by 100, we get:
100x = 12.222...
Subtracting x from both sides, we get:
99x = 12.1
Dividing both sides by 99, we get:
x = 12.1/99
x = 4/33
Therefore, 0.1222 repeating is equal to the fraction 4/33.
Understanding the Concept
The reason why 0.1222 repeating can be converted to a fraction is because it has a finite sequence of digits that repeats indefinitely. This sequence can be captured by a fraction with a denominator that is a multiple of the length of the sequence.
In this case, the sequence "22" has a length of 2, so the denominator of the fraction is 33 (a multiple of 2). The numerator, 4, is the initial part of the decimal before the sequence starts repeating.
Conclusion
In conclusion, 0.1222 repeating is equal to the fraction 4/33. This conversion is possible due to the periodic nature of the decimal, which allows us to capture it with a simple fraction. Understanding this concept can help us appreciate the beauty and simplicity of mathematics.
