Question

This is a decimal that neither terminates nor repeats.

This is a terminating decimal.

This is a repeating decimal.

0.581372...

And .4444…

Answer 1

Can they be written as a fraction

Answer 2

Let's analyze the given decimals based on the characteristics of their representations:

1. **Neither Terminating nor Repeating**: This refers to decimals that cannot be expressed as a fraction of two integers and do not exhibit a repeating pattern. An example of such a number is the decimal representation of \(\pi\) (approximately 3.14159...) or \( \sqrt{2} \) (approximately 1.41421...), which goes on forever without repeating.

2. **Terminating Decimal**: A terminating decimal is one that comes to an end after a finite number of digits. For example, the decimal \(0.75\) is a terminating decimal because it has only two decimal places.

3. **Repeating Decimal**: A repeating decimal has a finite block of digits that repeat indefinitely. For example, \(0.4444...\) (which can be represented as \(\frac{4}{9}\)) is a repeating decimal since the digit 4 repeats forever.

Now, examining your specific examples:

- **0.581372...**: If it is stated like this, it appears to have no repeating or terminating pattern given it implies that it continues without repeating. Therefore, it would be classified as neither terminating nor repeating, unless further context indicates the repeating pattern of the digits.

- **.4444…**: This is clearly a repeating decimal. The digit 4 repeats indefinitely.

In summary:

- **0.581372...** - Neither terminating nor repeating
- **.4444...** - Repeating decimal