Question
Identify the most specific set to which each of the following numbers belongs:(5 points)
A. 6.263
B. 42−−√
C. 4.56666....
D. 0
E. 36−−−√
F. 9/11
G. -25
1. Irrational number
2. natural number
3. rational number
4. integer
5. whole number
A. 6.263
B. 42−−√
C. 4.56666....
D. 0
E. 36−−−√
F. 9/11
G. -25
1. Irrational number
2. natural number
3. rational number
4. integer
5. whole number
Answers
GPT-4o mini
Let's categorize each number based on the sets provided:
A. **6.263**
- This is a decimal number that can be expressed as a fraction (6263/1000).
- It is a **rational number (3)**.
B. **42−−√ (the square root of 42)**
- The square root of 42 is not a perfect square and cannot be expressed as a fraction of integers.
- It is an **irrational number (1)**.
C. **4.56666....** (which indicates a repeating decimal)
- This number can be expressed as a fraction (since it has a repeating decimal).
- It is a **rational number (3)**.
D. **0**
- Zero is an integer, a whole number, and can also be considered a rational number because it can be expressed as a fraction (0/1).
- The most specific set is **integer (4)**.
E. **36−−−√ (the square root of 36)**
- The square root of 36 is 6, which is a whole number and an integer.
- The most specific set is **natural number (2)** (if we consider natural numbers as starting from 1, 6 is an integer; if natural numbers include 0, it still qualifies as an integer).
F. **9/11**
- This number is expressed as a fraction of two integers.
- It is a **rational number (3)**.
G. **-25**
- This is an integer, but it is not a whole number or a natural number because negative numbers do not belong to those sets.
- It belongs to the most specific set, which is **integer (4)**.
So here is the final categorization:
A. 6.263 → **3 (rational number)**
B. 42−−√ → **1 (irrational number)**
C. 4.56666.... → **3 (rational number)**
D. 0 → **4 (integer)**
E. 36−−−√ → **2 (natural number)**
F. 9/11 → **3 (rational number)**
G. -25 → **4 (integer)**
A. **6.263**
- This is a decimal number that can be expressed as a fraction (6263/1000).
- It is a **rational number (3)**.
B. **42−−√ (the square root of 42)**
- The square root of 42 is not a perfect square and cannot be expressed as a fraction of integers.
- It is an **irrational number (1)**.
C. **4.56666....** (which indicates a repeating decimal)
- This number can be expressed as a fraction (since it has a repeating decimal).
- It is a **rational number (3)**.
D. **0**
- Zero is an integer, a whole number, and can also be considered a rational number because it can be expressed as a fraction (0/1).
- The most specific set is **integer (4)**.
E. **36−−−√ (the square root of 36)**
- The square root of 36 is 6, which is a whole number and an integer.
- The most specific set is **natural number (2)** (if we consider natural numbers as starting from 1, 6 is an integer; if natural numbers include 0, it still qualifies as an integer).
F. **9/11**
- This number is expressed as a fraction of two integers.
- It is a **rational number (3)**.
G. **-25**
- This is an integer, but it is not a whole number or a natural number because negative numbers do not belong to those sets.
- It belongs to the most specific set, which is **integer (4)**.
So here is the final categorization:
A. 6.263 → **3 (rational number)**
B. 42−−√ → **1 (irrational number)**
C. 4.56666.... → **3 (rational number)**
D. 0 → **4 (integer)**
E. 36−−−√ → **2 (natural number)**
F. 9/11 → **3 (rational number)**
G. -25 → **4 (integer)**