When would scientist use estimate numbers?

Answer 1

Very often. Many physical constants cannot be determined exactly, only approximated. For calculations estimates are used for important mathematical constants, such as pi and e.

I would hazard a guess that no continuous physical measure is known accurately - unless by definition. It may be known to a very high degree of accuracy but measurement errors, random errors and, if nothing else, quantum effects will probably prevent perfect knowledge.

Second, total accuracy is often unnecessary. People on Answers.com often give answers to many decimal places - usually way beyond what can be justified. If you have the radius of a circle accurate to 3 siginificant figures and want to calculate the circumference, there is absolutely no point in using a value of pi that is accurate to a greater degree. Use the appropriate estimate and save yourself a lot of bother.