Question
rational numbers cannot
be negative
go on forever and ever
repeat digits in the decimal
be square roots of non-perfect squares
be negative
go on forever and ever
repeat digits in the decimal
be square roots of non-perfect squares
Answers
GPT-4o mini
Let's evaluate each statement regarding rational numbers:
1. **Rational numbers cannot be negative**: This statement is **false**. Rational numbers can be negative. For example, \(-\frac{1}{2}\) is a rational number.
2. **Rational numbers go on forever and ever**: This statement is **partially true**. Rational numbers themselves do not go on forever; however, their decimal representations can either terminate (like \(0.5\)) or repeat (like \(0.333...\) for \(\frac{1}{3}\)).
3. **Rational numbers repeat digits in the decimal**: This statement is **true**. The decimal representation of a rational number either terminates or repeats (is periodic).
4. **Rational numbers be square roots of non-perfect squares**: This statement is **false**. The square root of a non-perfect square (like \(\sqrt{2}\)) is not a rational number; it is irrational.
In summary, rational numbers can be negative and do not go on forever in the sense of not being represented as fractions; they have specific decimal representations—either terminating or repeating. They also cannot be the square roots of non-perfect squares.
1. **Rational numbers cannot be negative**: This statement is **false**. Rational numbers can be negative. For example, \(-\frac{1}{2}\) is a rational number.
2. **Rational numbers go on forever and ever**: This statement is **partially true**. Rational numbers themselves do not go on forever; however, their decimal representations can either terminate (like \(0.5\)) or repeat (like \(0.333...\) for \(\frac{1}{3}\)).
3. **Rational numbers repeat digits in the decimal**: This statement is **true**. The decimal representation of a rational number either terminates or repeats (is periodic).
4. **Rational numbers be square roots of non-perfect squares**: This statement is **false**. The square root of a non-perfect square (like \(\sqrt{2}\)) is not a rational number; it is irrational.
In summary, rational numbers can be negative and do not go on forever in the sense of not being represented as fractions; they have specific decimal representations—either terminating or repeating. They also cannot be the square roots of non-perfect squares.