Which rational number also belongs to the set of natural numbers?
Select one: A. 15 B. -12 C. 38 D. 0.1666…
The Correct Answer and Explanation is:
The correct answer is A. 15.
Explanation:
Natural Numbers:
Natural numbers are the set of positive integers that start from 1 and go up to infinity (1, 2, 3, 4, …). They do not include zero, negative numbers, or fractions. The natural numbers are often used for counting and ordering. In some definitions, the set of natural numbers includes zero (0, 1, 2, 3, …), but the more traditional view excludes zero.
Rational Numbers:
Rational numbers are numbers that can be expressed as the quotient or fraction ( \frac{p}{q} ), where ( p ) is an integer and ( q ) is a non-zero integer. This means that all integers, finite decimals, and repeating decimals fall into the category of rational numbers. Examples include ( \frac{1}{2} ), 3 (which can be expressed as ( \frac{3}{1} )), and 0.333… (which can be expressed as ( \frac{1}{3} )).
Analysis of the Options:
- A. 15: This is a positive integer and can be expressed as ( \frac{15}{1} ). Therefore, it is both a natural number and a rational number.
- B. -12: While -12 is a rational number (as it can be written as ( \frac{-12}{1} )), it is not a natural number because natural numbers are only positive.
- C. 38: Like 15, 38 is a positive integer and can be written as ( \frac{38}{1} ). However, it is not the best choice in this context because we are looking for just one number from the options given.
- D. 0.1666…: This represents a repeating decimal, specifically ( \frac{1}{6} ). It is rational but not a natural number.
In conclusion, option A. 15 is the only choice that belongs to both the set of natural numbers and the set of rational numbers, as it is a positive integer and can be expressed as a fraction with a denominator of one.