Identifying the Repeating Decimal- A Guide to Choosing the Correct Example

Which one of the following examples represents a repeating decimal?

In the world of mathematics, decimals play a crucial role in representing numbers that are not whole. While some decimals terminate, meaning they have a finite number of digits after the decimal point, others repeat indefinitely. Identifying a repeating decimal is an essential skill in understanding decimal arithmetic and its applications in various fields. This article aims to explore different examples and help you determine which one represents a repeating decimal.

Repeating decimals are characterized by a sequence of digits that repeats indefinitely. For instance, consider the decimal 0.3333… (where the digit 3 repeats infinitely). This is a classic example of a repeating decimal. Another example is 0.142857142857… (where the sequence 142857 repeats indefinitely).

Now, let’s analyze some examples to determine which one represents a repeating decimal:

1. 0.3333…
2. 0.6666…
3. 0.25
4. 0.333…

Which one of these examples represents a repeating decimal? If you guessed 0.3333… and 0.6666…, you are correct. Both of these examples have a repeating sequence of digits (3 and 6, respectively). On the other hand, 0.25 is a terminating decimal, as it has a finite number of digits after the decimal point. Similarly, 0.333… is also a repeating decimal, as the digit 3 repeats indefinitely.

Understanding the difference between repeating and terminating decimals is vital in various mathematical operations, such as adding, subtracting, multiplying, and dividing decimals. Moreover, recognizing repeating decimals can help us solve real-world problems, such as calculating interest rates or measuring distances.

In conclusion, when faced with the question “which one of the following examples represents a repeating decimal,” it is crucial to identify the sequence of digits that repeats indefinitely. By analyzing the given examples, we can determine that 0.3333… and 0.6666… are the repeating decimals in this list. Familiarizing yourself with such examples will undoubtedly enhance your mathematical skills and enable you to tackle more complex problems with ease.