Question
Which of the following are rational numbers?
A. 194.265
B. √289
C. π
D. 765.4
A. 194.265
B. √289
C. π
D. 765.4
Answers
GPT-4o mini
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.
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.