This may be too trivial to ask. But when I searched, I didn't find anyone asking this question previously on this site.
When I consider 3.0 and 3.00, from a mathematical perspective, absolutely I can see both of them being equal. But some long time ago, I heard that those two are actually not equal in a scientific perspective, because they differ in number of significant digits after decimal point. Now, I wanted to know is this claim correct? Or just a hoax?
Mathematically, they are the same.
However, in real life, with concrete measurements, you never know exactly which number you actually have. You're uncertain. And it is considered good practice to keep track of how uncertain.
If I'm measuring the width of a nail with a ruler, and I get 3mm, then I have no idea whether it's actually 3.15 or 2.8 or something in-between. It's just impossible to tell. In that case, i would report it as 3mm, and not 3.00mm because that would be dishonest.
If I'm measuring the length of a piece of wood with a measuring tape, and as far as I can see it matches perfectly with the 3m mark, then I can tell that it isn't 3.01m and it isn't 2.99m. in that case I can confidently report it as 3.00m (maybe even 3.000m, but that would be pushing it). If I just said 3m, then someone listening might not appreciate that I have sub-centimeter precision, as opposed to, say, just looking at the plank and guessing the length from experience.