Identify whether the given numbers belongs to the given set.
Natural Numbers
Whole Numbers
Integers
Rational Numbers
−11
2.45
1
−117
Natural Numbers: No (natural numbers are positive integers, so -11 and -117 are not natural numbers)
Whole Numbers: No (whole numbers include 0 and positive integers, so -11 and -117 are not whole numbers)
Integers: Yes (-11 and -117 are integers because they are whole numbers that can be negative)
Rational Numbers: Yes (-11 and -117 are rational numbers because they can be expressed as a ratio of two integers, -11/-1 and -117/-1, respectively)
The given numbers can be classified as follows:
Natural Numbers: 1
Whole Numbers: 1
Integers: -11, 1, -117
Rational Numbers: 2.45, 1, -117
To identify whether the given numbers belong to a specific set, we will determine the characteristics and inclusion criteria for each set.
1. Natural Numbers:
- Natural numbers are the set of positive integers, starting from 1 and continuing indefinitely.
- Natural numbers do not include zero or negative numbers.
Given numbers: -11, 2.45, 1, -117
Explanation:
- The number -11 is not a natural number because natural numbers do not include negative numbers. Therefore, -11 does not belong to the set of natural numbers.
- The number 2.45 is not a natural number because natural numbers only include whole numbers without any decimal or fractional part. Therefore, 2.45 does not belong to the set of natural numbers.
- The number 1 is a natural number because it is a positive integer. Therefore, 1 belongs to the set of natural numbers.
- The number -117 is not a natural number because natural numbers do not include negative numbers. Therefore, -117 does not belong to the set of natural numbers.
2. Whole Numbers:
- Whole numbers are the set of non-negative integers, including zero.
- Whole numbers do not include negative numbers or fractional parts.
Given numbers: -11, 2.45, 1, -117
Explanation:
- The number -11 is not a whole number because whole numbers do not include negative numbers. Therefore, -11 does not belong to the set of whole numbers.
- The number 2.45 is not a whole number because whole numbers do not include decimal or fractional parts. Therefore, 2.45 does not belong to the set of whole numbers.
- The number 1 is a whole number because it is a non-negative integer. Therefore, 1 belongs to the set of whole numbers.
- The number -117 is not a whole number because whole numbers do not include negative numbers. Therefore, -117 does not belong to the set of whole numbers.
3. Integers:
- Integers are the set of positive and negative whole numbers, including zero.
Given numbers: -11, 2.45, 1, -117
Explanation:
- The number -11 is an integer because it is a negative whole number. Therefore, -11 belongs to the set of integers.
- The number 2.45 is not an integer because integers do not include decimal or fractional parts. Therefore, 2.45 does not belong to the set of integers.
- The number 1 is an integer because it is a positive whole number. Therefore, 1 belongs to the set of integers.
- The number -117 is an integer because it is a negative whole number. Therefore, -117 belongs to the set of integers.
4. Rational Numbers:
- Rational numbers are the set of numbers that can be expressed as a fraction of two integers, where the denominator is not zero.
Given numbers: -11, 2.45, 1, -117
Explanation:
- The number -11 is a rational number because it can be expressed as the fraction -11/1. Therefore, -11 belongs to the set of rational numbers.
- The number 2.45 is a rational number because it can be expressed as the fraction 245/100. Therefore, 2.45 belongs to the set of rational numbers.
- The number 1 is a rational number because it can be expressed as the fraction 1/1. Therefore, 1 belongs to the set of rational numbers.
- The number -117 is a rational number because it can be expressed as the fraction -117/1. Therefore, -117 belongs to the set of rational numbers.
Summary:
- The number -11 belongs to the sets of integers and rational numbers but not natural numbers or whole numbers.
- The number 2.45 belongs only to the set of rational numbers.
- The number 1 belongs to the sets of natural numbers, whole numbers, integers, and rational numbers.
- The number -117 belongs to the sets of integers and rational numbers but not natural numbers or whole numbers.