The Number System Unit Test
Math 8 Q1 (Pre-Algebra) / The Number System
Which statement is true about the relationships between the number sets?(1 point)
Responses
All rational numbers are also integers.
Whole numbers include all natural numbers and 0.
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
The statement "Whole numbers include all natural numbers and 0." is true.
rip on answer yet
The statement that is true about the relationships between the number sets is:
Whole numbers include all natural numbers and 0.
To determine which statement is true about the relationships between the number sets, we can break down each statement and analyze it:
1. All rational numbers are also integers.
To determine if this statement is true, we need to understand the definitions of rational numbers and integers. Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Integers, on the other hand, include all whole numbers (positive, negative, or zero) and their opposites. Based on this definition, it is not true that all rational numbers are also integers. For example, the number 1/2 is a rational number but not an integer. Therefore, this statement is false.
2. Whole numbers include all natural numbers and 0.
To determine if this statement is true, we need to understand the definitions of whole numbers and natural numbers. Whole numbers include all positive numbers and zero. Natural numbers, on the other hand, are the positive integers starting from 1. Since all natural numbers are included in the definition of whole numbers, and zero is also included, this statement is true.
3. Not all natural numbers are real numbers.
To determine if this statement is true, we need to understand the definitions of natural numbers and real numbers. Natural numbers are the positive integers starting from 1. Real numbers, on the other hand, include all rational and irrational numbers. Since all natural numbers can be expressed as rational numbers, and rational numbers are a subset of real numbers, it is true that not all natural numbers are real numbers.
4. Some irrational numbers are also integers.
To determine if this statement is true, we need to understand the definitions of irrational numbers and integers. Irrational numbers cannot be expressed as a fraction and have non-repeating and non-terminating decimal expansions. Integers, as mentioned earlier, include all whole numbers and their opposites. Since all integers can be expressed as fractions (e.g., 2 = 2/1), they are not irrational. Therefore, this statement is false.
Based on the analysis above, the statement that is true about the relationships between the number sets is:
- Whole numbers include all natural numbers and 0.