Final answer:
The statement that is always true is that all integers are whole numbers. The number that is both an integer and a rational number is 17/2. The number that does not belong in the whole number box but would belong in the natural number box is 0.
Step-by-step explanation:
To determine which statement is always true, let's analyze each option:
a. All integers are whole numbers. This statement is true, as integers include all whole numbers and their negatives.
b. All rational numbers are integers. This statement is false, as rational numbers include fractions, decimals, and integers.
c. Irrational numbers can be integers. This statement is false, as irrational numbers cannot be expressed as a fraction or a ratio of integers.
d. All natural numbers are whole numbers. This statement is true, as natural numbers include positive integers and zero.
Therefore, the correct answer is a. All integers are whole numbers.
To identify a number that is both an integer and a rational number, we need to understand the properties of each:
- An integer is a whole number that can be positive, negative, or zero.
- A rational number is a number that can be expressed as a fraction, where the numerator and denominator are integers.
Looking at the options:
a. -17.6: This number is not an integer, as it is a decimal.
b. 17/2: This number is both an integer (-17) and a rational number, as it can be expressed as a fraction.
c. √(-121): This number is irrational, as it involves taking the square root of a negative number.
d. √(-136): This number is also irrational, as it involves taking the square root of a negative number.
Therefore, the number that is both an integer and a rational number is b. 17/2.
To determine the number that does not belong in the whole number box but would belong in the natural number box, we need to understand the definitions of each:
- Whole numbers include all positive integers and zero.
- Natural numbers include all positive integers, excluding zero.
Looking at the options:
a. -15/3: This number is not a whole number, as it is a fraction.
b. -208.3: This number is not a whole number, as it is a decimal.
c. 12: This number is both a whole number and a natural number.
d. 0: This number is a whole number, but it is not a natural number, as natural numbers exclude zero.
Therefore, the number that does not belong in the whole number box but would belong in the natural number box is d. 0.