To determine which of the given numbers are rational, we need to remember that a rational number is any number that can be expressed as the quotient of two integers (i.e., a fraction where the numerator and the denominator are both integers), or as a terminating or repeating decimal.
Let's evaluate each option:
A. 194.265 - This is a terminating decimal and can be expressed as 194265/1000. Therefore, it is a rational number.
B. √289 - The square root of 289 is 17, which is an integer. Thus, it can be expressed as 17/1. Therefore, it is a rational number.
C. π - Pi is an irrational number because it cannot be expressed as a fraction of two integers and its decimal representation is non-terminating and non-repeating. Therefore, it is not a rational number.
D. 765.4 - This is also a terminating decimal and can be expressed as 7654/10. Therefore, it is a rational number.
Based on this analysis, the rational numbers among the options are:
- A. 194.265
- B. √289
- D. 765.4
Thus, the rational numbers are A, B, and D.