1.2 Sets of Real Numbers
Write all names that apply to each number.
8.
9.
10. Tell whether the statement “All integers are rational numbers” is true
or false. Explain your choice.

Ask by Carlson Bowen. in the United States

Jan 24,2025

Question

1.2 Sets of Real Numbers
Write all names that apply to each number.
8.
9.
10. Tell whether the statement “All integers are rational numbers” is true
or false. Explain your choice.

Ask by Carlson Bowen. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

Let's analyze each part of the problem step by step.

### 8. $$ \frac{121}{\sqrt{121}} $$

First, we simplify the expression:

$$
\sqrt{121} = 11
$$

Now substituting this back into the expression:

$$
\frac{121}{\sqrt{121}} = \frac{121}{11} = 11
$$

Now, we can identify the types of numbers that apply to $$ 11 $$:

- **Natural Number**: $$ 11 $$ is a positive integer, so it is a natural number.
- **Whole Number**: $$ 11 $$ is a natural number, and all natural numbers are whole numbers.
- **Integer**: $$ 11 $$ is a whole number, and all whole numbers are integers.
- **Rational Number**: $$ 11 $$ can be expressed as $$ \frac{11}{1} $$, which is a ratio of two integers.
- **Real Number**: All rational numbers are also real numbers.

### Summary for 8:
- Natural Number
- Whole Number
- Integer
- Rational Number
- Real Number

---

### 9. $$ \frac{\pi}{2} $$

The number $$ \frac{\pi}{2} $$ is a bit different. Let's analyze it:

- **Irrational Number**: $$ \pi $$ is known to be an irrational number, and dividing an irrational number by a non-zero integer (in this case, $$ 2 $$) results in another irrational number. Therefore, $$ \frac{\pi}{2} $$ is irrational.
- **Rational Number**: $$ \frac{\pi}{2} $$ cannot be expressed as a ratio of two integers, so it is not a rational number.
- **Real Number**: All irrational numbers are also real numbers.

### Summary for 9:
- Irrational Number
- Real Number

---

### 10. Statement: "All integers are rational numbers"

This statement is **true**.

**Explanation**: 
- A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. 
- Since any integer $$ n $$ can be expressed as $$ \frac{n}{1} $$, it follows that all integers can be represented as rational numbers.

### Final Summary:
- For $$ \frac{121}{\sqrt{121}} $$: Natural Number, Whole Number, Integer, Rational Number, Real Number.
- For $$ \frac{\pi}{2} $$: Irrational Number, Real Number.
- The statement "All integers are rational numbers" is true.
- **8. $$ \frac{121}{\sqrt{121}} $$:** Natural Number, Whole Number, Integer, Rational Number, Real Number. - **9. $$ \frac{\pi}{2} $$:** Irrational Number, Real Number. - **10. "All integers are rational numbers":** True.

1.2 Sets of Real Numbers
Write all names that apply to each number.
8.
9.
10. Tell whether the statement “All integers are rational numbers” is true
or false. Explain your choice.

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1.2 Sets of Real Numbers Write all names that apply to each number. 8. 9. 10. Tell whether the statement “All integers are rational numbers” is true or false. Explain your choice.

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1.2 Sets of Real Numbers
Write all names that apply to each number.
8.
9.
10. Tell whether the statement “All integers are rational numbers” is true
or false. Explain your choice.