Which of the following statements is true?
The ratio of two integers is an irrational number.
An irrational number is a non-terminating, non-repeating decimal.
A perfect square is an irrational number.
Rational numbers are always positive.
The statement "An irrational number is a non-terminating, non-repeating decimal." is true.
Here's a breakdown of each statement:
1. The ratio of two integers is an irrational number.
This statement is false. The ratio of two integers is actually a rational number, provided the denominator is not zero. A rational number can be expressed as a fraction with integer numerator and a nonzero integer denominator. Some ratios of integers can be irrational, but not all ratios are.
2. An irrational number is a non-terminating, non-repeating decimal.
This statement is true. By definition, an irrational number cannot be expressed as a fraction of two integers, and when written in decimal form, it does not terminate nor repeat.
3. A perfect square is an irrational number.
This statement is false. A perfect square refers to a number that is the square of an integer. For example, 4 (which is 2 squared) and 9 (which is 3 squared) are perfect squares and they are rational.
4. Rational numbers are always positive.
This statement is false. Rational numbers can be positive, negative, or zero. As long as a number can be expressed as a fraction of two integers with the denominator not equal to zero, it is rational. Examples include -1/3, 0 (which can be written as 0/1), and 2 (which can be written as 2/1).