Which statement is true about the relationships between the number sets?(1 point)
Responses
All integers are also rational numbers.
All integers are also rational numbers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all positive integers and negative integers.
All integers are also rational numbers.
Which of the following is true about 9?(1 point)
Responses
It is both an integer and a whole number.
It is both an integer and a whole number.
It is an integer but not a rational number.
It is an integer but not a rational number.
It is a whole number but not an integer.
It is a whole number but not an integer.
It is an integer but not a whole number.
It is both an integer and a whole number.
Four people have found the distance in kilometers across a small bridge using different methods.
Their results are given in the table. Order the distances from least to greatest.
(1 point)
Responses
512, 28−−√, 5.5¯¯¯, 234
512, 28−−√, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234
28−−√, 5.5¯¯¯, 234, 512
28−−√, 5.5¯¯¯, 234, 512
234 , 5.5¯¯¯, 28−−√, 512
5.5¯¯¯, 28−−√, 234, 512
The statement that is true about the relationships between the number sets is:
All integers are also rational numbers.
To determine which statement is true about the relationships between the number sets, we can analyze each option.
Option 1: "All integers are also rational numbers."
To determine if this statement is true, we need to understand the definitions of integers and rational numbers. Integers are whole numbers (both positive and negative) and zero, while rational numbers are numbers that can be expressed as a ratio of two integers. Since all integers can be represented as a ratio of themselves and 1 (e.g., 5/1, -7/1, 0/1), it is correct to say that all integers are also rational numbers. Therefore, this statement is true.
Option 2: "Not all natural numbers are real numbers."
To determine the truth of this statement, we need to understand the definitions of natural numbers and real numbers. Natural numbers are the counting numbers starting from 1 (1, 2, 3, 4, ...), while real numbers include all rational and irrational numbers. As natural numbers are a subset of real numbers, it is correct to say that not all natural numbers are real numbers. Thus, this statement is true.
Option 3: "Some irrational numbers are also integers."
To assess the accuracy of this statement, we need to recall that irrational numbers are numbers that cannot be expressed as a simple fraction or ratio of two integers. In contrast, integers are whole numbers (both positive and negative) and zero. Since there is no overlap between integers and irrational numbers, it is incorrect to say that some irrational numbers are also integers. Thus, this statement is false.
Option 4: "Whole numbers include all positive integers and negative integers."
To verify the truth of this statement, we need to understand the definition of whole numbers. Whole numbers are similar to integers but do not include negative numbers. They include zero and positive integers (0, 1, 2, 3, ...). Therefore, it is incorrect to say that whole numbers include negative integers. Hence, this statement is false.
Based on the explanations provided, we can conclude that the true statement about the relationships between the number sets is: "All integers are also rational numbers."