Question
Rational numbers cannot
be negative
go on forever and ever
repeat digits in the decimal
• be square roots of non-perfect squares
_. (1 point)
be negative
go on forever and ever
repeat digits in the decimal
• be square roots of non-perfect squares
_. (1 point)
Answers
GPT-4o mini
Rational numbers are defined as numbers that can be expressed as the quotient of two integers \( \frac{a}{b} \), where \( a \) is an integer and \( b \) is a non-zero integer. Based on this definition, let's evaluate the statements you provided:
1. **Cannot be negative**: This is false. Rational numbers can be negative. For example, \(-\frac{1}{2}\) is a negative rational number.
2. **Go on forever and ever**: This statement is somewhat misleading. Rational numbers can have decimal representations that either terminate (like \(0.5\)) or repeat (like \(0.333...\)). They do not necessarily "go on forever" in a non-repeating sense, which refers to irrational numbers.
3. **Repeat digits in the decimal**: This is true. One of the defining characteristics of rational numbers is that their decimal representation either terminates or eventually repeats.
4. **Be square roots of non-perfect squares**: This is false. The square root of a non-perfect square (like \(\sqrt{2}\)) is irrational, not rational.
Based on the evaluation above, only the statement about repeating digits in the decimal representation is correct.
1. **Cannot be negative**: This is false. Rational numbers can be negative. For example, \(-\frac{1}{2}\) is a negative rational number.
2. **Go on forever and ever**: This statement is somewhat misleading. Rational numbers can have decimal representations that either terminate (like \(0.5\)) or repeat (like \(0.333...\)). They do not necessarily "go on forever" in a non-repeating sense, which refers to irrational numbers.
3. **Repeat digits in the decimal**: This is true. One of the defining characteristics of rational numbers is that their decimal representation either terminates or eventually repeats.
4. **Be square roots of non-perfect squares**: This is false. The square root of a non-perfect square (like \(\sqrt{2}\)) is irrational, not rational.
Based on the evaluation above, only the statement about repeating digits in the decimal representation is correct.