Re: Question for those who might have the knowledge
Spectra of the radiation.
If you heat up something (gas, tungsten) to around 2700K, it glows orange-white. Heat it to 6000K, it glows yellow-white, 10000K, blueish.
There's a very specific shape to this "black body" spectrum, check Wikipedia.
As to the round numbers - it's because the scientists don't claim more precision than they have actually measured.