Question

For 1 through 8, classify each number in as many categories as possible.
6. -9/3
7. √2
8.___
5.678
9. Is 1/45 to the left or the right of O on a number line?
10. Is -0.001 to the left or the right of O on a number line.

Answer 1

Let's analyze and classify each number from 6 to 8:

### Number 6: -9/3
1. **Integer**: -3 (since -9/3 = -3)
2. **Rational Number**: Can be expressed as a fraction (-3/1).
3. **Real Number**: All integers and rational numbers are real numbers.
4. **Negative Number**: Since it is less than zero.

### Number 7: √2
1. **Irrational Number**: Cannot be expressed as a simple fraction.
2. **Real Number**: All irrational numbers are real numbers.
3. **Positive Number**: Since √2 is approximately 1.414, which is greater than 0.

### Number 8: 5.678
1. **Decimal**: It contains a decimal point.
2. **Rational Number**: Can be expressed as a fraction (5678/1000).
3. **Real Number**: All rational numbers are real numbers.
4. **Positive Number**: Greater than zero.

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### Number 9: 1/45 on a number line
- **Location**: 1/45 is a positive number (approximately 0.0222), so it is **to the right of 0** on a number line.

### Number 10: -0.001 on a number line
- **Location**: -0.001 is a negative number, so it is **to the left of 0** on a number line.

If you need further clarifications or more details about each classification, feel free to ask!