Question
The Real Number System - 4/6
Streak bonus!
+15
4 of 4
Which of these numbers is rational? Select all that apply.
square 4
2.156987129. . .
0.6 upperlined
square 5
Streak bonus!
+15
4 of 4
Which of these numbers is rational? Select all that apply.
square 4
2.156987129. . .
0.6 upperlined
square 5
Answers
Answered by
GPT-4o mini
To determine which of the given numbers are rational, we need to recall that a rational number is any number that can be expressed as the quotient of two integers (i.e., a fraction where the denominator is not zero).
Let's analyze the options:
1. **square 4**: The square root of 4 is 2, which is a rational number (since it can be expressed as \( \frac{2}{1} \)).
2. **2.156987129...**: This is a non-repeating, non-terminating decimal, which means it cannot be expressed as a fraction of two integers. Therefore, it is not a rational number.
3. **0.6 upperlined**: This notation indicates that the digit 6 repeats (i.e., \(0.666...\)). This can be expressed as the fraction \( \frac{2}{3} \), making it a rational number.
4. **square 5**: The square root of 5 is an irrational number because it cannot be expressed as a fraction of two integers.
Based on this analysis, the rational numbers from the given list are:
- **square 4**
- **0.6 upperlined**
Let's analyze the options:
1. **square 4**: The square root of 4 is 2, which is a rational number (since it can be expressed as \( \frac{2}{1} \)).
2. **2.156987129...**: This is a non-repeating, non-terminating decimal, which means it cannot be expressed as a fraction of two integers. Therefore, it is not a rational number.
3. **0.6 upperlined**: This notation indicates that the digit 6 repeats (i.e., \(0.666...\)). This can be expressed as the fraction \( \frac{2}{3} \), making it a rational number.
4. **square 5**: The square root of 5 is an irrational number because it cannot be expressed as a fraction of two integers.
Based on this analysis, the rational numbers from the given list are:
- **square 4**
- **0.6 upperlined**