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.
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.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
The last statement is true: Whole numbers include all natural numbers and 0.
Well, well, well, let's see what we've got here! It seems like we stumbled upon a quiz! Now, let's have some fun with these statements!
Statement 1: All rational numbers are also integers. Ha! Nope, that's not true at all! Rational numbers are numbers that can be expressed as a fraction, while integers are just the whole numbers, positive or negative. So sorry, statement 1, you're barking up the wrong number line!
Statement 2: Some irrational numbers are also integers. Oh boy, now we're talking nonsense! Irrational numbers are numbers that can't be expressed as fractions, and they go on forever without repeating. So, saying that some irrational numbers are integers is like saying some unicorns are also zebras. It's a wild claim, but I'm afraid it's not true!
Statement 3: Not all natural numbers are real numbers. Ah, good old statement 3! You're on the right track! Natural numbers are those beautiful, positive integers. But guess what? Real numbers include all the rational and irrational numbers as well. So, statement 3, you're absolutely right! Not all natural numbers make it to the "real" party!
Statement 4: Whole numbers include all natural numbers and 0. Well, statement 4, you're quite the smarty pants! Whole numbers are just the natural numbers along with the added bonus of zero. So, you got it spot on! Whole numbers are a friendly bunch that welcome all the naturals and that big ol' zero.
So, there you have it! Statement 1 and 2 are far from the truth, but statement 3 and 4 are spot on! Now let's move on to the next question, shall we? Good luck!
The correct statement is: Whole numbers include all natural numbers and 0.
To determine which statement is true about the relationships between the number sets, we need to understand the definitions of each set.
1. Rational numbers: These are numbers that can be expressed as a fraction or a ratio of two integers. For example, 1/2, -3/4, and 5 are all rational numbers.
2. Integers: These are whole numbers (both positive and negative) and zero. For example, -2, 0, and 5 are all integers.
3. Irrational numbers: These are numbers that cannot be expressed as a fraction or a ratio of two integers. They cannot be written as terminating or repeating decimals. For example, √2, π, and e are all irrational numbers.
4. Natural numbers: These are positive integers excluding zero. For example, 1, 2, 3, and so on.
5. Real numbers: These are all rational and irrational numbers combined. They include fractions, decimals, integers, and irrational numbers.
Now let's evaluate each statement:
a. "All rational numbers are also integers." This statement is false. Rational numbers include fractions, which are not integers. So, there are rational numbers that are not integers.
b. "Some irrational numbers are also integers." This statement is false. By definition, irrational numbers cannot be expressed as integers.
c. "Not all natural numbers are real numbers." This statement is false. Natural numbers are a subset of real numbers. Therefore, all natural numbers are also real numbers.
d. "Whole numbers include all natural numbers and 0." This statement is true. Whole numbers are a set that includes all natural numbers (positive integers) and zero.
Therefore, the correct statement is: "Whole numbers include all natural numbers and 0."