Question
For each number, determine if it can be written as a fraction. Then state the reason.
Can this be written
as a fraction? Reason
Yes
No
This is a terminating decimal.
This is a repeating decimal.
This is a decimal that neither terminates nor repeats.
Yes
No
This is a terminating decimal.
This is a repeating decimal.
This is a decimal that neither terminates nor repeats.
Yes
No
This is a terminating decimal.
This is a repeating decimal.
This is a decimal that neither terminates nor repeats.
Yes
No
This is a terminating decimal.
This is a repeating decimal.
This is a decimal that neither terminates nor repeats.
Can this be written
as a fraction? Reason
Yes
No
This is a terminating decimal.
This is a repeating decimal.
This is a decimal that neither terminates nor repeats.
Yes
No
This is a terminating decimal.
This is a repeating decimal.
This is a decimal that neither terminates nor repeats.
Yes
No
This is a terminating decimal.
This is a repeating decimal.
This is a decimal that neither terminates nor repeats.
Yes
No
This is a terminating decimal.
This is a repeating decimal.
This is a decimal that neither terminates nor repeats.
Answers
GPT-4o mini
To determine if a number can be written as a fraction (i.e., expressed as a rational number), we can analyze its decimal representation. Here’s how we can categorize them:
1. **Terminating Decimal**: A decimal that ends after a finite number of digits (e.g., 0.25, 0.5). These can be expressed as fractions.
2. **Repeating Decimal**: A decimal that has a digit or group of digits that repeat indefinitely (e.g., 0.333..., 0.666...). These can also be expressed as fractions.
3. **Non-terminating, Non-repeating Decimal**: A decimal that continues indefinitely without repeating any pattern (e.g., π, √2). These cannot be expressed as fractions and are classified as irrational numbers.
Given these definitions, let's analyze the cases listed.
| Can this be written as a fraction? | Reason |
|------------------------------------|-------------------------------------------|
| Yes | This is a terminating decimal. |
| Yes | This is a repeating decimal. |
| No | This is a decimal that neither terminates nor repeats. |
| Yes | This is a terminating decimal. |
| Yes | This is a repeating decimal. |
| No | This is a decimal that neither terminates nor repeats. |
| Yes | This is a terminating decimal. |
| Yes | This is a repeating decimal. |
| No | This is a decimal that neither terminates nor repeats. |
| Yes | This is a terminating decimal. |
To fill out the table appropriately for specific numbers, we would need the exact numbers themselves in order to classify them correctly as terminating, repeating, or non-terminating/ non-repeating. Please provide the specific numbers you'd like analyzed.
1. **Terminating Decimal**: A decimal that ends after a finite number of digits (e.g., 0.25, 0.5). These can be expressed as fractions.
2. **Repeating Decimal**: A decimal that has a digit or group of digits that repeat indefinitely (e.g., 0.333..., 0.666...). These can also be expressed as fractions.
3. **Non-terminating, Non-repeating Decimal**: A decimal that continues indefinitely without repeating any pattern (e.g., π, √2). These cannot be expressed as fractions and are classified as irrational numbers.
Given these definitions, let's analyze the cases listed.
| Can this be written as a fraction? | Reason |
|------------------------------------|-------------------------------------------|
| Yes | This is a terminating decimal. |
| Yes | This is a repeating decimal. |
| No | This is a decimal that neither terminates nor repeats. |
| Yes | This is a terminating decimal. |
| Yes | This is a repeating decimal. |
| No | This is a decimal that neither terminates nor repeats. |
| Yes | This is a terminating decimal. |
| Yes | This is a repeating decimal. |
| No | This is a decimal that neither terminates nor repeats. |
| Yes | This is a terminating decimal. |
To fill out the table appropriately for specific numbers, we would need the exact numbers themselves in order to classify them correctly as terminating, repeating, or non-terminating/ non-repeating. Please provide the specific numbers you'd like analyzed.