Question

Determine if 0, point, 9, 3, 7, 50.9375 is rational or irrational and give a reason for your answer.

Answer 1

To determine whether the numbers 0, point, 9, 3, 7, and 50.9375 are rational or irrational, we need to understand the definitions of rational and irrational numbers.

- **Rational numbers** are numbers that can be expressed as the quotient or fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \) is not zero. This includes integers, fractions, and finite decimals.
- **Irrational numbers** are numbers that cannot be expressed as a simple fraction. They are non-repeating and non-terminating decimals.

Now, analyzing each of the numbers:

1. **0**: This is a rational number because it can be expressed as \( \frac{0}{1} \).
2. **point**: This term seems unclear. If it's intended to refer to a decimal point without a subsequent number, it is not a number in itself. If it refers to a decimal representation (like 0. or similar), then it is often treated as 0, which is rational. Otherwise, it cannot be determined.
3. **9**: This is also a rational number, as it can be expressed as \( \frac{9}{1} \).
4. **3**: This is a rational number, since it can be expressed as \( \frac{3}{1} \).
5. **7**: This is a rational number, as it can be expressed as \( \frac{7}{1} \).
6. **50.9375**: This is a finite decimal and can be expressed as a fraction \( \frac{509375}{10000} \). Therefore, it is a rational number.

In conclusion, all the numbers listed (assuming point refers to 0 or is clarified) are rational numbers. If "point" is a reference to a decimal without meaning, that remains indeterminate, but assuming it refers to 0, only 0 falls into a gray area based on representation. The other specific numbers are definitively rational.