Today I had a physics lecture. The professor kept going on about the importance of significant figures. They show how accurate the measurment is, writing more than necessary misleads people as to how accurate it is, etc, etc, etc. He said he saw a student get an F on his paper once because he put the wrong number of significant figures on it and the professor was furious. After class I asked him how important significant figures are when there are no measurments. He responded everything comes from some measurment, so I asked him about problems with no units what so ever. He didn't have an answer, but reiterated how crucial they are in general.

I asked this question on Chemistry Stack Exachange, and one person answered:

The step-by-step approach is to consider each step separately (observing the correct order of priority), keeping track of significant figures of the intermediate results. Then, calculate the number without any rounding of the intermediate results, and record it with the appropriate number

2.00 x 30) + 5.01 + 2.0

The product has two significant figures, least significant figure is the ones.

Adding 5.01 will have least significant figure as the ones.

Adding 2.0 will have least significant figure as the ones.

The arithmetic result (unrounded) is 67.01, so you write down 6.7⋅10^1. Depending who your teacher is, 67 or 67. is fine as well.

But 30 only has 1 significant figure. It doesn't make sense. I feel like there's something really obvious nobody is telling me.

Edit:He fixed it and wrote the answer should be 7 x 10^1. That makes a lot more sense. My rounding was off. I think I have a slightly better handle on this now.