.21 as a Repeating Decimal: Exploring Its Fractional Equivalent
Introduction
Repeating decimals, also known as recurring decimals, are a fascinating aspect of mathematics. They are decimal numbers that have a sequence of digits that repeat indefinitely. In this article, we will delve into the world of repeating decimals and explore the fractional equivalent of .21, a simple yet intriguing example.
What is .21 as a Repeating Decimal?
.21 is a repeating decimal, meaning that it has a sequence of digits that repeat indefinitely. The repeating pattern in this case is 21, which means that the decimal can be written as:
.212121...
Converting .21 to a Fraction
To convert .21 to a fraction, we can use a few different methods. One popular approach is to multiply the decimal by a power of 10, such as 100, and then simplify the resulting fraction.
Let's do this with .21:
.21 × 100 = 21
Now, we can simplify the fraction:
21 ÷ 99 = 2/9
So, .21 as a repeating decimal is equal to the fraction 2/9.
Properties of the Fraction 2/9
Now that we have converted .21 to a fraction, let's explore some properties of the resulting fraction, 2/9.
- Equivalent Ratios: The fraction 2/9 is equivalent to other ratios, such as 4/18, 6/27, and so on. These ratios all represent the same proportional relationship.
- Decimal Expansion: When we divide the numerator (2) by the denominator (9), we get the original decimal: .21.
- Simplification: The fraction 2/9 is already in its simplest form, meaning that it cannot be simplified further.
Conclusion
In conclusion, .21 as a repeating decimal is equivalent to the fraction 2/9. By converting the decimal to a fraction, we can explore the properties and relationships of the resulting fraction, gaining a deeper understanding of the underlying mathematics. Repeating decimals, such as .21, serve as a fascinating gateway to the world of fractions, providing a unique perspective on the intricate web of mathematical relationships.
