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:
- 0: This is a rational number because it can be expressed as \( \frac{0}{1} \).
- 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.
- 9: This is also a rational number, as it can be expressed as \( \frac{9}{1} \).
- 3: This is a rational number, since it can be expressed as \( \frac{3}{1} \).
- 7: This is a rational number, as it can be expressed as \( \frac{7}{1} \).
- 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.
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