To which set of numbers does the number belong?
-1.875 Select one:
A. integers b. natural numbers
. rational numbers
D. irrational numbers
To which set of numbers does the number belong? −15/13
(that’s a fraction, by the way) Select one: a. rational numbers b. natural numbers c. integers d. irrational numbers
The Correct Answer and Explanation is:
Question 1: To which set of numbers does the number -1.875 belong?
Answer: C. Rational Numbers
Explanation:
The number -1.875 belongs to the set of rational numbers. Rational numbers are defined as any numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. This means that a rational number can be written in the form (\frac{p}{q}), where (p) and (q) are integers, and (q \neq 0).
In the case of -1.875, it can be expressed as (-\frac{1875}{1000}) or further simplified to (-\frac{15}{8}). Both forms demonstrate that -1.875 can indeed be written as a fraction of integers, meeting the criteria for rational numbers.
In contrast, integers include whole numbers and their negative counterparts, such as -1, 0, 1, etc. Since -1.875 is not a whole number, it cannot belong to the set of integers. Natural numbers are positive integers starting from 1 (1, 2, 3, …) and thus do not include negative numbers or fractions. Finally, irrational numbers are those that cannot be expressed as a fraction of two integers, like the square root of 2 or (\pi), which does not apply to -1.875.
Question 2: To which set of numbers does the number -15/13 belong?
Answer: A. Rational Numbers
Explanation:
The fraction -15/13 is also classified as a rational number. Similar to the first example, a rational number is any number that can be expressed as the ratio of two integers. In this case, -15/13 meets the definition because it is the quotient of the integer -15 (the numerator) and the integer 13 (the denominator), with the condition that the denominator is not zero.
This fraction clearly illustrates that it is part of the rational number set since it can be written in the form (\frac{p}{q}). It is important to note that the sign of the fraction (negative in this case) does not change its classification as a rational number. Furthermore, -15/13 is not a natural number, as natural numbers are always positive and start from 1. It is also not an integer because it is not a whole number, and irrational numbers cannot be represented as fractions, which -15/13 clearly is.
Both -1.875 and -15/13 belong to the set of rational numbers due to their ability to be expressed as fractions of integers, showcasing the diversity within the rational number category.