Select all sets in which the number 3/7 is an element.
A integers
B. rational numbers
c. natural numbers
D. real numbers
E. irrational numbers
F. whole numbers
The Correct Answer and Explanation is:
To determine the sets in which the number ( \frac{3}{7} ) is an element, let’s analyze each option:
A. Integers
Integers are whole numbers that can be positive, negative, or zero. They include numbers like (-2, -1, 0, 1, 2), etc. However, ( \frac{3}{7} ) is a fraction and not a whole number, so it is not an integer.
B. Rational Numbers
Rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Since ( \frac{3}{7} ) can be expressed in this form (where 3 is the numerator and 7 is the denominator), it is a rational number.
C. Natural Numbers
Natural numbers are the positive integers starting from 1 (i.e., ( 1, 2, 3, \ldots )). They do not include fractions or negative numbers. Since ( \frac{3}{7} ) is not a whole number, it is not a natural number.
D. Real Numbers
Real numbers include all rational and irrational numbers. Since ( \frac{3}{7} ) is a rational number, it is also classified as a real number.
E. Irrational Numbers
Irrational numbers are numbers that cannot be expressed as a fraction of integers. Examples include numbers like ( \pi ) and ( \sqrt{2} ). Since ( \frac{3}{7} ) can be expressed as a fraction, it is not an irrational number.
F. Whole Numbers
Whole numbers include all natural numbers along with zero (i.e., ( 0, 1, 2, 3, \ldots )). As ( \frac{3}{7} ) is a fraction and not a whole number, it is not a whole number.
Summary
From the analysis, the sets in which ( \frac{3}{7} ) is an element are:
- B. Rational Numbers
- D. Real Numbers
To conclude, the number ( \frac{3}{7} ) belongs to the sets of rational numbers and real numbers because it can be expressed as a fraction of integers, which meets the criteria for these sets. However, it does not belong to the sets of integers, natural numbers, whole numbers, or irrational numbers.