Question

Which numbers are rational? Check the three that apply.(3 points)Responsesπpi2.72 point 7112311 over 2314−−√square root of 1472−−√square root of 7236−−√

Answer 1

To determine which numbers are rational, we need to identify whether each number can be expressed as a fraction of two integers (a/b, where a and b are integers and b ≠ 0).

1. **π (pi)**: This is an irrational number; it cannot be expressed as a fraction of two integers. **Not rational.**

2. **2.7**: This can be expressed as \( \frac{27}{10} \), so it is a rational number. **Rational.**

3. **2.7112311**: This is a decimal that terminates, so it can also be expressed as a fraction. Therefore, it is rational. **Rational.**

4. **\( \frac{11}{23} \)**: This is already in the form of a fraction, with both numbers being integers. **Rational.**

5. **\( \sqrt{14} \)**: This is an irrational number because 14 is not a perfect square. **Not rational.**

6. **\( \sqrt{7} \)**: This is also irrational because 7 is not a perfect square. **Not rational.**

7. **36**: This is an integer and can be expressed as \( \frac{36}{1} \). **Rational.**

In summary, the rational numbers in the list are:
- **2.7**
- **2.7112311**
- **\( \frac{11}{23} \)**
- **36**

So, the three that apply as rational numbers are:
1. **2.7**
2. **2.7112311**
3. **\( \frac{11}{23} \)**