to which subsets of the real numbers does each number belong?

A. 15 natural numbers, whole numbers, integers, rational numbers
B. -1.4583 rational numbers (since -1.4583 is a terminating decimal)
C. 57 squared irrational numbers (since 57 is not a perfect square)

1 answer

Let's categorize each of the given numbers into their appropriate subsets of the real numbers:

A. 15

  • Natural Numbers: Yes, 15 is a natural number.
  • Whole Numbers: Yes, whole numbers include all natural numbers and zero.
  • Integers: Yes, integers include all whole numbers and their negative counterparts.
  • Rational Numbers: Yes, 15 can be expressed as a fraction (e.g., 15/1).

So, 15 belongs to the subsets: Natural numbers, Whole numbers, Integers, Rational numbers.


B. -1.4583

  • Natural Numbers: No, it is negative.
  • Whole Numbers: No, it is negative.
  • Integers: No, it is not a whole number or a non-negative integer.
  • Rational Numbers: Yes, -1.4583 is a rational number because it can be expressed as a fraction (-14583/10000), and it is a terminating decimal.

So, -1.4583 belongs to the subset: Rational numbers.


C. 57 squared

  • 57 squared equals \( 57^2 = 3249 \).
  • Natural Numbers: Yes, it is positive.
  • Whole Numbers: Yes, it is a whole number.
  • Integers: Yes, it is an integer.
  • Rational Numbers: Yes, it can be expressed as a fraction (e.g., 3249/1).
  • Irrational Numbers: No, 3249 is a perfect square (it is the square of 57), thus it is not an irrational number.

So, 57 squared (3249) belongs to the subsets: Natural numbers, Whole numbers, Integers, Rational numbers.

To summarize:

  • A. 15: Natural numbers, Whole numbers, Integers, Rational numbers.
  • B. -1.4583: Rational numbers.
  • C. 57 squared (3249): Natural numbers, Whole numbers, Integers, Rational numbers.