Question

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

Answer 1

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