0.12 as a Repeating Fraction
A repeating fraction, also known as a recurring decimal, is a decimal number that has a sequence of digits that repeats indefinitely. In this article, we will explore the repeating fraction representation of 0.12.
What is 0.12 as a Repeating Fraction?
The decimal number 0.12 can be written as a repeating fraction by dividing the numerator 12 by the denominator 99. Yes, you read that right - 99!
The Calculation
Let's do the calculation to find the repeating fraction representation of 0.12:
12 ÷ 99 = 0.121212...
As you can see, the decimal number 0.12 can be written as a repeating fraction with the sequence 12 repeating indefinitely.
Why Does 0.12 Have a Repeating Fraction?
The reason 0.12 has a repeating fraction is due to the nature of decimal numbers. When you divide a numerator by a denominator, the result is a decimal number that can be either terminating or repeating. In this case, 12 divided by 99 results in a repeating sequence of digits.
Properties of Repeating Fractions
Repeating fractions have some interesting properties:
- They are rational numbers: Repeating fractions can be expressed as a ratio of integers, i.e., a fraction.
- They have a finite decimal representation: Although the decimal representation may seem infinite, it can be expressed as a finite fraction.
- They are periodic: The sequence of digits in a repeating fraction repeats in a predictable and periodic manner.
Conclusion
In conclusion, 0.12 as a repeating fraction is a fascinating representation of a decimal number. By dividing 12 by 99, we can express 0.12 as a repeating fraction with the sequence 12 repeating indefinitely. This representation highlights the properties of repeating fractions, including their rationality, finite decimal representation, and periodicity.
