Which statement is true about the relationships between the number sets?(1 point)
Responses
All irrational numbers are whole numbers.
All irrational numbers are whole numbers.
Some natural numbers are irrational numbers.
Some natural numbers are irrational numbers.
Some integers are irrational numbers.
Some integers are irrational numbers.
All rational numbers are real numbers.
All the statements are true, except for the statement "All irrational numbers are whole numbers."
The correct statement is: All rational numbers are real numbers.
Monique measured the widths of several stamps in her collection of world stamps. The measurements are 158in., 11116in., 134in., and 112in. What is the width of the widest stamp?
The statement that is true about the relationships between the number sets is: All rational numbers are real numbers.
The statement that is true about the relationships between the number sets is: "All rational numbers are real numbers."
To understand why this statement is true, we need to know the definitions of rational and real numbers.
Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They can be either positive or negative, and they include integers and fractions.
Real numbers, on the other hand, include both rational numbers and irrational numbers. Real numbers can be represented on a number line, and they include numbers that cannot be expressed as fractions, such as square roots of non-perfect squares, like √2 or π.
Since rational numbers are a subset of real numbers (they are included within the set of real numbers), it is true to say that all rational numbers are real numbers.
To determine the truth of the other statements:
- "All irrational numbers are whole numbers" is false. Irrational numbers cannot be expressed as fractions, and whole numbers are integers without fractions or decimals. Therefore, they are distinct sets.
- "Some natural numbers are irrational numbers" is also false. Natural numbers (also known as counting numbers) are positive integers, and irrational numbers cannot be expressed as fractions or decimals. Therefore, there is no overlap between these number sets.
- "Some integers are irrational numbers" is true. Some integers can be irrational numbers, such as √2 or -√3. However, it is important to note that not all integers are irrational numbers.
So, of the given options, the statement that is true is: "All rational numbers are real numbers."