Name The Subsets Of The Real Numbers To Which Each Number Belongs:
A.-2.324
B.Square Root Of 46
I don't even know what this stuff means. Please help!
A) Real/Rational
B) Real/Irrational
because -2.324 = (-2324/1000)
but sqrt(46) cannot be expressed as a fraction
There are various classes of numbers. In order of increasing "size" we have
whole numbers: 1,2,3,4,...
integers: ...-3,-2,-1,0,1,2,3,...
rational numbers (fractions): 1/2, 3/7, 98/113, etc
Rational numbers include also
terminating decimals: 2.5, 123.456, 99.32764, etc.
repeating decimals: 1.22222..., 9831279.2397239239239...
irrational numbers: everything else. They are decimal numbers which go on forever without repeating. Such as
√7 = 2.64575...
π = 3.14159265...
and so on
roots may be rational or even integers, if the radicand is a perfect power:
√36 = 6 because 6^2 = 36
√2.25 = 1.5 because 1.5^2 = 2.25
∛27 = 3 because 3^3 = 27
and so forth
Oh, don't worry! I'm here to help you, and we'll make it fun, I promise!
Let's break it down. The real numbers are simply all the numbers that exist, including rational and irrational numbers. So, A = -2.324 and B = √46.
Now, let's figure out which subsets these numbers belong to, just for fun:
A = -2.324:
- It's a real number because it's a normal, everyday number.
- It's also a decimal number since it has a decimal point.
- It's not a natural number because natural numbers are positive whole numbers (1, 2, 3, and so on).
- It's not an even number because it doesn't end with 0, 2, 4, 6, or 8.
- It's not an odd number because it's not divisible by 2.
- It's not a prime number because it's divisible by some other numbers (like -1, -2, and -2.324 itself).
- It's not the number zero because it's not equal to 0.
B = √46:
- Like A, it's a real number because it's a normal number.
- It's not a natural number because the square root of 46 is not an integer.
- It's not an even number because the square root of 46 is not divisible by 2.
- It's not an odd number because the square root of 46 is not an integer.
- It's not a prime number because it's not a whole number, and it's divisible by other numbers (like -1, 1, and the square root of 46 itself).
- It's not the number zero because the square root of 46 is not equal to 0.
So, to summarize:
A belongs to the subset of real numbers that are not natural, even, odd, prime, or zero.
B belongs to the subset of real numbers that are not natural, even, odd, prime, or zero either.
And there you have it! I hope I could make it a bit more enjoyable for you. If you have any more questions, feel free to ask!
Sure! Understanding subsets of real numbers and determining which subset a given number belongs to can be a bit challenging if you're new to this concept. Let's break it down:
1. Real Numbers: The real numbers include all rational and irrational numbers, which means it encompasses practically every number you can think of, including whole numbers, integers, fractions, decimals, and square roots of non-perfect squares.
2. Subsets: Subsets are smaller groups within a larger set. In the case of real numbers, there are several subsets, such as natural numbers (N), whole numbers (W), integers (Z), rational numbers (Q), and irrational numbers (I).
Now, let's determine which subsets the given numbers belong to:
A. -2.324:
- Since -2.324 is a decimal number, it falls under the subset of real numbers.
- It is also a rational number because it can be expressed as a fraction (e.g., -2324/1000) with both the numerator and the denominator as integers.
- Therefore, -2.324 belongs to the subset of real numbers (R) and the subset of rational numbers (Q).
B. Square Root of 46:
- The square root of 46 is an irrational number because it cannot be expressed as a fraction or a terminating/repeating decimal.
- Therefore, the square root of 46 belongs to the subset of real numbers (R) and the subset of irrational numbers (I).
To summarize:
A. -2.324 belongs to the subsets R and Q.
B. Square Root of 46 belongs to the subsets R and I.
Remember, having a basic understanding of subsets and the properties of different types of numbers will help you categorize numbers more easily.