Question

Determine if 0, point, 6, 2, 50.625 is rational or irrational and give a reason for your answer.

Answer 1

To determine if the numbers 0, point (which is likely intended to be 0.0), 6, 2, and 50.625 are rational or irrational, we must first understand the definitions of these types of numbers.

Rational numbers are numbers that can be expressed as the quotient of two integers, that is, in the form \( \frac{p}{q} \) where \( p \) and \( q \) are integers, and \( q \) is not zero. Irrational numbers, on the other hand, cannot be expressed in that form and have non-repeating, non-terminating decimal expansions.

Now let's evaluate each number:

1. **0**: This can be expressed as \( \frac{0}{1} \), which is a valid expression of a rational number. Hence, 0 is rational.

2. **0.0**: This is equivalent to 0, and therefore also rational for the same reason.

3. **6**: This can be expressed as \( \frac{6}{1} \), which is a rational number. Thus, 6 is rational.

4. **2**: This can be expressed as \( \frac{2}{1} \), which is a rational number. Therefore, 2 is also rational.

5. **50.625**: This can be expressed as \( \frac{50625}{1000} \) (since 50.625 is equivalent to 50.625/1). The numerator (50625) and the denominator (1000) are both integers, and the denominator is not zero. Thus, 50.625 is rational.

In summary, all of the given numbers (0, 0.0, 6, 2, and 50.625) are **rational numbers**.