Question

Which of the following is a rational number: 2π, 6/0, 61−−√, or 0.37815? (1 point)

Answer 1

A rational number is defined as a number that can be expressed as the quotient of two integers (i.e., it can be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \)).

Let's analyze each option:

1. **\( 2\pi \)**: This is an irrational number because \(\pi\) is irrational and multiplying by 2 does not change its nature.

2. **\( \frac{6}{0} \)**: This expression is undefined because division by zero is not permissible.

3. **\( \sqrt{61} \)**: This is also an irrational number since 61 is not a perfect square.

4. **\( 0.37815 \)**: This is a decimal number that can be expressed as a fraction (e.g., \( \frac{37815}{100000} \)), which makes it a rational number.

Therefore, the rational number from the options provided is **0.37815**.