What characterizes a rational number?

What characterizes a rational number?

• A. It cannot be expressed as a fraction
• B. It can be expressed as the quotient of two integers
• C. It is always a whole number
• D. It is an infinite decimal

Answer: (B)

A rational number is defined as any number that can be expressed as the quotient of two integers, where the numerator is an integer and the denominator is a non-zero integer. This characteristic is fundamental because it means that rational numbers include a wide variety of values, such as whole numbers (which can be expressed as a fraction with a denominator of 1), fractions, and terminating or repeating decimals. For instance, the number 1 can be expressed as 1/1, and the fraction 3/4 is also a rational number since both 3 and 4 are integers and 4 is not zero. Additionally, repeating decimals, such as 0.333..., can be expressed as 1/3, further illustrating the nature of rational numbers. Therefore, the correct answer emphasizes the fundamental property of rational numbers, which is their ability to be represented as fractions involving integers, contrasting with other options that do not accurately capture the essence of rationality in numbers.

A rational number is defined as any number that can be expressed as the quotient of two integers, where the numerator is an integer and the denominator is a non-zero integer. This characteristic is fundamental because it means that rational numbers include a wide variety of values, such as whole numbers (which can be expressed as a fraction with a denominator of 1), fractions, and terminating or repeating decimals.

For instance, the number 1 can be expressed as 1/1, and the fraction 3/4 is also a rational number since both 3 and 4 are integers and 4 is not zero. Additionally, repeating decimals, such as 0.333..., can be expressed as 1/3, further illustrating the nature of rational numbers.

Therefore, the correct answer emphasizes the fundamental property of rational numbers, which is their ability to be represented as fractions involving integers, contrasting with other options that do not accurately capture the essence of rationality in numbers.