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. \( \frac{11}{23} \)