Question

Which of the following are rational numbers?
194.265
\sqrt{ 289}
\pi
765.4

Answer 1

To determine which of the given numbers are rational, let's review the definitions:

- A rational number is any number that can be expressed as the quotient of two integers (i.e., in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \)).

Let's analyze each of the numbers provided:

1. **194.265**: This is a terminating decimal and can be expressed as the fraction \( \frac{194265}{1000} \). Hence, it is a rational number.

2. **\(\sqrt{289}\)**: The square root of 289 is 17 (since \( 17 \times 17 = 289 \)), which is an integer. All integers are rational numbers. Thus, \(\sqrt{289}\) is a rational number.

3. **\(\pi\)**: The number \(\pi\) is an irrational number as it cannot be expressed as a fraction of two integers. Therefore, it is not a rational number.

4. **765.4**: This is also a terminating decimal and can be expressed as the fraction \( \frac{7654}{10} \). Hence, it is a rational number.

In conclusion, the rational numbers among the given options are:
- 194.265
- \(\sqrt{289}\)
- 765.4

\(\pi\) is not a rational number.