Question

Determine which categories that the following numbers belong. A number may be in more than one category. Click Here for Help Video.

0
0


Natural


Whole


Integer


Rational


Irrational

6
6


Natural


Whole


Integer


Rational


Irrational

−
1
−1


Natural


Whole


Integer


Rational


Irrational

1
−
4
−4
1
​



Natural


Whole


Integer


Rational


Irrational

17
17
​

Answer 1

Let's categorize each of the given numbers based on the classifications provided.

1. **0**
- Natural: No (natural numbers are positive integers starting from 1)
- Whole: Yes (whole numbers include 0 and positive integers)
- Integer: Yes (integers include whole numbers and negative integers)
- Rational: Yes (0 can be expressed as 0/1, which is a fraction)
- Irrational: No (irrational numbers cannot be expressed as a simple fraction)

**Categories:** Whole, Integer, Rational

2. **6**
- Natural: Yes (6 is a positive integer)
- Whole: Yes (6 is a whole number)
- Integer: Yes (6 is an integer)
- Rational: Yes (6 can be expressed as 6/1, which is a fraction)
- Irrational: No (6 is a rational number)

**Categories:** Natural, Whole, Integer, Rational

3. **−1**
- Natural: No (natural numbers are only positive integers)
- Whole: No (whole numbers are non-negative, which do not include negative integers)
- Integer: Yes (−1 is an integer)
- Rational: Yes (−1 can be expressed as −1/1, which is a fraction)
- Irrational: No (−1 is a rational number)

**Categories:** Integer, Rational

4. **1/4**
- Natural: No (not a whole positive integer)
- Whole: No (not a whole number)
- Integer: No (not an integer)
- Rational: Yes (1/4 is a fraction)
- Irrational: No (1/4 is a rational number)

**Categories:** Rational

5. **17**
- Natural: Yes (17 is a positive integer)
- Whole: Yes (17 is a whole number)
- Integer: Yes (17 is an integer)
- Rational: Yes (17 can be expressed as 17/1, which is a fraction)
- Irrational: No (17 is a rational number)

**Categories:** Natural, Whole, Integer, Rational

### Summary of Categories:
- **0:** Whole, Integer, Rational
- **6:** Natural, Whole, Integer, Rational
- **−1:** Integer, Rational
- **1/4:** Rational
- **17:** Natural, Whole, Integer, Rational