{-11,-6 1/3, -5, 0,0.14,3 5/6,5,square root 7,9} what are the irrational numbers, integers, rational numbers?

Let's categorize the numbers into irrational numbers, integers, and rational numbers.

### Given Set: 
\[
\{-11, -6 \frac{1}{3}, -5, 0, 0.14, 3 \frac{5}{6}, 5, \sqrt{7}, 9\}
\]

### 1. **Irrational Numbers:**
Irrational numbers cannot be expressed as a fraction of two integers. They have non-terminating, non-repeating decimal expansions.
- \(\sqrt{7}\)

**Irrational numbers**: \(\{\sqrt{7}\}\)

### 2. **Integers:**
Integers are whole numbers, including positive numbers, negative numbers, and zero.
- \(-11\)
- \(-5\)
- \(0\)
- \(5\)
- \(9\)

**Integers**: \(\{-11, -5, 0, 5, 9\}\)

### 3. **Rational Numbers:**
Rational numbers can be expressed as a fraction of two integers. They have either terminating or repeating decimal expansions.
- \(-11\) (integer)
- \(-6 \frac{1}{3} = -\frac{19}{3}\)
- \(-5\) (integer)
- \(0\) (integer)
- \(0.14 = \frac{14}{100} = \frac{7}{50}\)
- \(3 \frac{5}{6} = \frac{23}{6}\)
- \(5\) (integer)
- \(9\) (integer)

**Rational numbers**: \(\{-11, -6 \frac{1}{3}, -5, 0, 0.14, 3 \frac{5}{6}, 5, 9\}\)

### Summary:
- **Irrational numbers**: \(\{\sqrt{7}\}\)
- **Integers**: \(\{-11, -5, 0, 5, 9\}\)
- **Rational numbers**: \(\{-11, -6 \frac{1}{3}, -5, 0, 0.14, 3 \frac{5}{6}, 5, 9\}\)

Would you like more details or have any questions? 

Here are five related questions:
1. What are examples of irrational numbers other than square roots?
2. How do you determine if a number is rational or irrational?
3. Can a number be both rational and irrational? Why or why not?
4. Are all integers also rational numbers? Explain.
5. How do you express a repeating decimal as a fraction?

**Tip:** Remember that all integers are rational numbers, but not all rational numbers are integers!

Explore the classification of numbers into irrational, integer, and rational categories with examples such as square roots and fractions. Learn about their properties and how to distinguish them in mathematics. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation