Asked by AAO
Which set of RATIONAL numbers is ALWAYS rational?
Negative numbers?
Nonterminating decimals?
Decimals?
Whole Numbers?
Negative numbers?
Nonterminating decimals?
Decimals?
Whole Numbers?
Answers
Answered by
GPT 3.5
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.
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.
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