Which of the following is a rational number: 2π , 60 , 61−−√ , or 0.37815?(1 point)

Question

Which of the following is a rational number:  2π ,  60 ,  61−−√ , or 0.37815?(1 point)
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GPT-4o mini · Answer

A rational number is any number that can be expressed as a fraction $ \frac{a}{b} $, where $ a $ and $ b $ are integers and $ b \neq 0 $. Let's analyze each option:

$ 2\pi $: Pi ($ \pi $) is an irrational number. Therefore, $ 2\pi $ is also irrational.
60: This is an integer, and it can be expressed as $ \frac{60}{1} $, making it a rational number.
$ \sqrt{61} $: The square root of 61 is not a perfect square, hence $ \sqrt{61} $ is an irrational number.
0.37815: This is a terminating decimal, which can also be expressed as a fraction (e.g., $ \frac{37815}{100000} $). Therefore, it is a rational number.

Based on the analysis, the rational numbers in the list are:

60
0.37815

Thus, among the options provided, 60 is a rational number.

mama j · Answer

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GPT-4o mini · Answer

I apologize if my previous response was not clear. Let's carefully review each option again to identify which is a rational number:

$ 2\pi $: This is an irrational number because $ \pi $ is not expressible as a fraction of two integers.
60: This is a whole number and can be expressed as $ \frac{60}{1} $, which makes it a rational number.
$ \sqrt{61} $: The square root of 61 is not a perfect square, so it is also an irrational number.
0.37815: This is a terminating decimal and can be expressed as a fraction (for example, $ \frac{37815}{100000} $), which makes it a rational number.

So, both 60 and 0.37815 are rational numbers. If you are looking for just one rational number from the list provided, 60 is a straightforward choice.

If you have a specific context or aspect you’d like me to focus on regarding rational numbers, feel free to clarify!