Which statement is true?
A. All irrational numbers are also rational numbers.
B. Half of the irrational numbers are also rational numbers.
C. One-third of the irrational numbers are also rational numbers.
D. Irrational numbers cannot be classified as rational numbers.
The correct statement is D. Irrational numbers cannot be classified as rational numbers.
To determine which statement is true, let's examine each option:
A. "All irrational numbers are also rational numbers."
This statement is false. By definition, rational numbers are numbers that can be expressed as a ratio of two integers. Irrational numbers, on the other hand, cannot be expressed as a simple fraction. Therefore, an irrational number cannot be classified as a rational number.
B. "Half of the irrational numbers are also rational numbers."
This statement is false as well. The set of irrational numbers is infinitely larger than the set of rational numbers since there are infinitely more irrational numbers between any two rational numbers. Therefore, it is not accurate to say that half of the irrational numbers are also rational numbers.
C. "One-third of the irrational numbers are also rational numbers."
This statement is also false. Just as with option B, the set of irrational numbers is much larger than the set of rational numbers. Any fraction, such as one-third, would not properly represent the relationship between these sets.
D. "Irrational numbers cannot be classified as rational numbers."
This statement is true. As mentioned earlier, irrational numbers cannot be expressed as a simple fraction, which is a requirement for being classified as a rational number. Hence, irrational numbers cannot be classified as rational.
Therefore, the correct answer is D. Irrational numbers cannot be classified as rational numbers.