Question

practice
directions: classify the following 16 numbers within the real number system.

1. 7
2. 0
3. -4
4. 12.5
5. \\(\sqrt{16}\\)
6. \\(\sqrt{2}\\)
7. \\(\pi\\)
8. -11
9. 3/4
10. -22/7
11. 5.333... (repeating decimal)
12. 1.272... (non-repeating, non-terminating)
13. 25
14. -0.6
15. 1000
16. \\(\sqrt{50}\\)

natural numbers:
whole numbers:
integers:
rational numbers:
irrational numbers:

Explanation:

Analyze and simplify the 16 given numbers

$$
LATEXBLOCK0
$$

Group numbers into the five real number subsets

$$
LATEXBLOCK1
$$

Answer:

Natural Numbers:
\(7\), \(\sqrt{16}\), \(25\), \(1000\)

Whole Numbers:
\(7\), \(0\), \(\sqrt{16}\), \(25\), \(1000\)

Integers:
\(7\), \(0\), \(-4\), \(\sqrt{16}\), \(-11\), \(25\), \(1000\)

Rational Numbers:
\(7\), \(0\), \(-4\), \(12.5\), \(\sqrt{16}\), \(-11\), \(3/4\), \(-22/7\), \(5.333...\), \(25\), \(-0.\bar{6}\), \(1000\)

Irrational Numbers:
\(\sqrt{2}\), \(\pi\), \(1.272...\), \(\sqrt{50}\)