For 1 through 8, classify each number in as many categories as possible.

1. -3
2. __
4.5
3. -4.89375872537653487287439843098…
4. -9.7654321
5. 1

1 answer

Let's classify each of the given numbers in different mathematical categories:

  1. -3

    • Integer: Yes (it is a whole number)
    • Rational Number: Yes (can be expressed as -3/1)
    • Real Number: Yes (it exists on the number line)
    • Negative Number: Yes (less than zero)
    • Whole Number: No (not non-negative)
  2. 4.5

    • Rational Number: Yes (can be expressed as 9/2)
    • Real Number: Yes (it exists on the number line)
    • Positive Number: Yes (greater than zero)
    • Decimal: Yes (it is in decimal form)
    • Not an Integer: No (it is not a whole number)
  3. -4.89375872537653487287439843098... (a repeating decimal)

    • Rational Number: No (it cannot be expressed as a fraction of two integers precisely due to the infinite decimal)
    • Real Number: Yes (it exists on the number line)
    • Negative Number: Yes (less than zero)
    • Decimal: Yes (it is in decimal form)
  4. -9.7654321

    • Rational Number: Yes (can be expressed as -97654321/10000000)
    • Real Number: Yes (it exists on the number line)
    • Negative Number: Yes (less than zero)
    • Decimal: Yes (it is in decimal form)
  5. 1

    • Integer: Yes (it is a whole number)
    • Rational Number: Yes (can be expressed as 1/1)
    • Real Number: Yes (it exists on the number line)
    • Positive Number: Yes (greater than zero)
    • Whole Number: Yes (it is non-negative)

In summary, the classifications for each number are as follows:

  1. -3: Integer, Rational Number, Real Number, Negative Number
  2. 4.5: Rational Number, Real Number, Positive Number, Decimal
  3. -4.89375872537653487287439843098…: Real Number, Negative Number, Decimal (Not rational)
  4. -9.7654321: Rational Number, Real Number, Negative Number, Decimal
  5. 1: Integer, Rational Number, Real Number, Positive Number, Whole Number