Do I have the right amount of sig digs?

[EgpYo]

Homework Statement

To simulate gravity a circular space station with a radius of 150m is rotated so that astronauts on the inner surface move at 30m/s. If a 75kg astronaut stands in a bathroom scale, what reading will it give? In Newtons.

Homework Equations

Fc = mv2/r

The Attempt at a Solution

Fc = Fg

Fg = mv2/r

Fg = (75)(900)/150

Fg = 450 N

Therefore the scale will say 450 N.

I don't get it... 30m/s is 1 sig dig. So my answer should be 400 N? Can somebody confirm this? It just seems weird to write "Therefore the scale will say 400 N" when in reality it will be 50 N greater, which is a big difference. I have to submit my answers for marking and I don't want to lose marks. So are you supposed to use sig digs even if it changes your answer a lot? Because there have been a few instances where I come across questions that should have 1 significant digit in the final answer but that would change my calculated answer by a lot.

 

[haruspex]

30m/s is 1 sig dig

Interpreting significant digits from the way numbers are shown is a bit tricky.
Ideally, it should be 3E1 (3*10¹) to show 1 sig dig, or 3.0E1 to show two, etc. I would take 30 as showing two.

 

[EgpYo]

Im going to ask you about another question, just to make sure I got the hang of this.

The question gives me 20m and 10m and my final answer was 22m. So this should stay as 22m? Because the only other way you could write 10m is 2x10^1. The fact that it is not written this way means the 0 should be considered significant? Thus, my final answer is 22m instead of 20m.

 

[EgpYo]

And going back to my original question, wouldn't that mean that 450 has 3 significant figures? Because using that same logic, ideally it should be written as 45x10^1

 

[haruspex]

Im going to ask you about another question, just to make sure I got the hang of this.

The question gives me 20m and 10m and my final answer was 22m. So this should stay as 22m? Because the only other way you could write 10m is 2x10^1. The fact that it is not written this way means the 0 should be considered significant? Thus, my final answer is 22m instead of 20m.

Yes.

And going back to my original question, wouldn't that mean that 450 has 3 significant figures? Because using that same logic, ideally it should be written as 45x10^1

Technically, but it would be a vindictive examiner that faulted you for answering 450.
(But I would prefer 4.5E2 to 45E1.)