Which of the following is a rational number?

Which of the following is a rational number?

• A. π
• B. √2
• C. 0.75
• D. e

Answer: (C)

A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, with the denominator being non-zero. In this case, 0.75 is a decimal representation that can be converted into a fraction. Specifically, 0.75 can be expressed as \( \frac{75}{100} \), which simplifies to \( \frac{3}{4} \). Both the numerator (3) and the denominator (4) are integers, satisfying the definition of a rational number. On the other hand, numbers such as π (pi) and e are known to be irrational. They cannot be expressed as a fraction of two integers. Similarly, √2 is also an irrational number because it cannot be accurately expressed as a fraction, despite being a well-known mathematical constant. This clear distinction places 0.75 as the only rational number among the given choices.

A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, with the denominator being non-zero.

In this case, 0.75 is a decimal representation that can be converted into a fraction. Specifically, 0.75 can be expressed as ( \frac{75}{100} ), which simplifies to ( \frac{3}{4} ). Both the numerator (3) and the denominator (4) are integers, satisfying the definition of a rational number.

On the other hand, numbers such as π (pi) and e are known to be irrational. They cannot be expressed as a fraction of two integers. Similarly, √2 is also an irrational number because it cannot be accurately expressed as a fraction, despite being a well-known mathematical constant. This clear distinction places 0.75 as the only rational number among the given choices.