Place the number sets in order from smalls to largest (1 point)
Integers
natural numbers
rational numbers
whole numbers
natural numbers -> whole numbers -> integers -> rational numbers
What's the answer
The correct order is:
natural numbers -> whole numbers -> integers -> rational numbers
Classify each number into its lowest possible category (5 points)
Natural numbers
whole numbers
integer
Rational numbers
irrational numbers
0,1.5,2,pi,-52
0: whole number, integer, rational number
1.5: rational number
2: whole number, integer, rational number
π (pi): irrational number
-52: integer, rational number
Fractions can be part of a whole number system
true or false
True. Fractions can be a part of the whole number system as they can be expressed as ratios of integers.
Of the following numbers, Which is an integer but does not belong in either of the subsets of integers: -13, 0, or 13?
Of the following numbers, 0 is the only number that is an integer but does not belong in either of the subsets of integers. Integers are typically classified as positive or negative whole numbers, but 0 is neither positive nor negative and is considered a separate subset. Therefore, -13 and 13 belong to the subset of negative and positive integers, respectively, while 0 does not.
To order the number sets from smallest to largest, it's helpful to understand the relationships between them. Here are the number sets you mentioned, along with their definitions:
1. Natural Numbers:
- Natural numbers, denoted by N, are the positive counting numbers: 1, 2, 3, 4, 5, ...
2. Whole Numbers:
- Whole numbers, denoted by W, include zero and all the natural numbers: 0, 1, 2, 3, 4, 5, ...
3. Integers:
- Integers, denoted by Z, include positive and negative whole numbers, including zero: ..., -3, -2, -1, 0, 1, 2, 3, ...
4. Rational Numbers:
- Rational numbers, denoted by Q, are numbers that can be expressed as fractions (quotients) of integers. This includes both terminating and repeating decimals, as well as whole numbers and natural numbers. For example: -2/3, 1/2, 0.75, 3, -8, ...
Now, let's order these sets from smallest to largest:
1. Natural numbers:
Natural numbers only include positive whole numbers. Therefore, they are the smallest set.
2. Whole numbers:
Whole numbers include zero and all the natural numbers. So, they are larger than natural numbers, but not as large as integers or rational numbers.
3. Integers:
Integers include both positive and negative whole numbers, and zero. Since integers include natural numbers and whole numbers, they are larger than both.
4. Rational numbers:
Rational numbers include both integers and fractions (quotients) of integers. This set is the largest among the four mentioned, as it encompasses all the other sets.
In summary, the correct order from smallest to largest is:
Natural numbers < Whole numbers < Integers < Rational numbers