What are rational numbers?

What are rational numbers?

• A. Numbers that cannot be expressed as fractions
• B. Numbers that can be written as a fraction
• C. Numbers that are always positive
• D. All whole numbers only

Answer: (B)

Rational numbers are defined as numbers that can be expressed as a fraction or a ratio of two integers, where the denominator is not zero. This means that any number that can be represented in the form \( \frac{a}{b} \) fits into the category of rational numbers, with \( a \) being any integer and \( b \) being any non-zero integer. This characterization includes various types of numbers: all integers (since any integer can be expressed as itself over 1), fractions (like \( \frac{1}{2} \)), and even terminating or repeating decimals (like 0.75 or 0.333...). The key aspect is the ability to express the number in a fractional form, which confirms that the correct answer covers the full range of rational numbers. In contrast, the other options misunderstand the definition of rational numbers in various ways, such as suggesting that they are exclusively positive or only whole numbers, or that they cannot be expressed as fractions, which does not hold true for rational numbers.

Rational numbers are defined as numbers that can be expressed as a fraction or a ratio of two integers, where the denominator is not zero. This means that any number that can be represented in the form ( \frac{a}{b} ) fits into the category of rational numbers, with ( a ) being any integer and ( b ) being any non-zero integer.

This characterization includes various types of numbers: all integers (since any integer can be expressed as itself over 1), fractions (like ( \frac{1}{2} )), and even terminating or repeating decimals (like 0.75 or 0.333...). The key aspect is the ability to express the number in a fractional form, which confirms that the correct answer covers the full range of rational numbers.

In contrast, the other options misunderstand the definition of rational numbers in various ways, such as suggesting that they are exclusively positive or only whole numbers, or that they cannot be expressed as fractions, which does not hold true for rational numbers.