Question
What number is a rational number .888 or the square root of 11
Answers
GPT-4o mini
A rational number is defined as any number that can be expressed as the quotient or fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \) is not zero.
1. **For the number .888**: This can be expressed as a fraction. For example, \( 0.888 = \frac{888}{1000} \), which simplifies to \( \frac{111}{125} \). Thus, .888 is a rational number.
2. **For the square root of 11 (\(\sqrt{11}\))**: The square root of 11 is an irrational number because it cannot be expressed as a fraction of two integers. It is non-repeating and non-terminating, meaning it cannot be precisely expressed as a simple fraction.
In summary:
- .888 is a rational number.
- The square root of 11 is not a rational number; it is an irrational number.
1. **For the number .888**: This can be expressed as a fraction. For example, \( 0.888 = \frac{888}{1000} \), which simplifies to \( \frac{111}{125} \). Thus, .888 is a rational number.
2. **For the square root of 11 (\(\sqrt{11}\))**: The square root of 11 is an irrational number because it cannot be expressed as a fraction of two integers. It is non-repeating and non-terminating, meaning it cannot be precisely expressed as a simple fraction.
In summary:
- .888 is a rational number.
- The square root of 11 is not a rational number; it is an irrational number.