Which set of RATIONAL numbers is ALWAYS rational?
Negative numbers?
Nonterminating decimals?
Decimals?
Whole Numbers?
The set of rational numbers is always rational.
Negative numbers: Negative rational numbers are rational numbers that can be expressed as a fraction where the numerator is a negative number and the denominator is a positive number. For example, -3/4 and -5/2 are negative rational numbers.
Nonterminating decimals: Nonterminating decimals can also be rational numbers if they can be expressed as fractions. For example, 0.5 can be written as 1/2 and is a rational number. However, not all nonterminating decimals are rational. For example, the decimal representation of pi (π) is nonterminating but cannot be expressed as a fraction, so it is not a rational number.
Decimals: Decimals can be either rational or irrational. Rational decimals are decimals that can be expressed as fractions, such as 0.25 (which is equivalent to 1/4). Irrational decimals cannot be expressed as fractions and have non-repeating, nonterminating decimal representations, such as √2 (approximately 1.41421356...).
Whole numbers: Whole numbers are actually a subset of integers, and integers are a subset of rational numbers. Whole numbers are always rational numbers because they can be expressed as fractions where the denominator is 1. For example, 3 can be written as 3/1, which is a rational number.
The set of rational numbers that are always rational includes whole numbers. Whole numbers are rational because they can be expressed as fractions with a denominator of 1. For example, 5 can be written as 5/1, which is a fraction and thus a rational number.
Negative numbers, nonterminating decimals, and decimals in general are not always rational. Negative numbers can be rational or irrational depending on whether they can be expressed as a fraction. Nonterminating decimals, such as the square root of 2 (1.41421356...) or pi (3.14159265...), are irrational because they cannot be expressed as a fraction. Decimals in general can be rational or irrational, depending on whether they terminate or repeat.