Which statement is true about the relationships between the number sets?(1 point) Responses All rational numbers are also integers. All rational numbers are also integers. Whole numbers include all natural numbers and 0. Whole numbers include all natural numbers and 0. Some irrational numbers are also integers. Some irrational numbers are also integers. Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
The statement "Not all natural numbers are real numbers" is true.
To determine which statement is true about the relationships between number sets, we will review each statement and explain the concepts involved.
1. "All rational numbers are also integers."
Explanation: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Integers are whole numbers that can be both positive and negative, including zero. This statement implies that every rational number is also an integer. However, this statement is false because rational numbers can be non-integer values, such as 1/2 or -3/4.
2. "Whole numbers include all natural numbers and 0."
Explanation: Whole numbers are similar to integers but do not include negative numbers. They start from zero and include all positive integers. Natural numbers are counting numbers, starting from 1 onward. This statement is true because whole numbers include all natural numbers and zero.
3. "Some irrational numbers are also integers."
Explanation: Irrational numbers are numbers that cannot be expressed as fractions or terminated decimals. They are non-repeating and non-terminating decimal numbers, such as π (pi) or √2 (square root of 2). Integers, as stated earlier, are whole numbers, including both positive and negative numbers. This statement is false because irrational numbers cannot be integers since they are non-integer values.
4. "Not all natural numbers are real numbers."
Explanation: Natural numbers, as mentioned before, are counting numbers starting from 1 onward. Real numbers encompass all numbers, including both rational and irrational numbers. This statement is false because all natural numbers are included in the set of real numbers.
Based on the explanations provided, the correct statement is: "Whole numbers include all natural numbers and 0."
Which of the following is true about −9 ?(1 point) Responses It is a whole number but not an integer. It is a whole number but not an integer. 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 whole number. It is an integer but not a whole number. It is an integer but not a rational number. It is an integer but not a rational number.
The statement "It is both an integer and a whole number" is true about -9.
A sign in a gas station advertises gas at the rate of $3.39910 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?(1 point)
To write the price strictly as a decimal, we can round the given price to the desired number of decimal places.
In this case, rounding to 2 decimal places, the price per gallon would be $3.40.