Let's take your question, "Would you know better if it said 5b km?". Nope, I wouldn't have a clue - or care!
ChatGPT informed me in SECONDS and 3-4 prompts that "At 2G constant accel/decel, it'll take ~8.5 days to get to Uranus, reaching a top speed of 2.3% of light speed (14.2 million m/s), and experiencing 17 seconds of time dilation."
Even if each of those numbers were off by a factor of two, it still gave me a greater intuition for the problem space than I had before.
I couldn't guess whether the flight time would be measured in days or years. With 4 prompts and 4 minutes invested, I had an answer within 11% (according to your sources, which I also didn't fact-check because it doesn't matter for this type of back-of-the-napkin work).
I didn't hide the fact of where this information came from - I cited my source. My hope was to share this new intuition of the problem space I'd received, so that HN viewers wouldn't have to invest even the small effort I did to enjoy these fun back-of-the-napkin numbers. The answer of <9 days was shocking to me!
Rather than banning intellectual curiosity and shunning use of our new amazing tools like ChatGPT/Claude/Bard/Mistral, I suggest we openly discuss and share our processes with each other. Who knows, maybe we'll learn something cool!