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)
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