Do I have the right amount of sig digs?

  • Thread starter EgpYo
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In summary, the circular space station with a radius of 150m is rotated to simulate gravity for astronauts on the inner surface. If a 75kg astronaut stands on a bathroom scale, it will read 450 N in Newtons. However, there is a discrepancy in the number of significant figures used in the question and answer, with the question stating a velocity of 30m/s, which should be considered as 1 significant digit, and the answer using 3 significant digits. This may result in a difference of 50 N in the final answer. The same issue arises in another question, where 20m and 10m were given and the final answer was 22m, which should be considered as 2 significant digits
  • #1
EgpYo
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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.
 
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  • #2
EgpYo said:
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.
 
  • #3
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.
 
  • #4
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
 
  • #5
EgpYo said:
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.
EgpYo said:
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.)
 

What are significant digits?

Significant digits, also known as significant figures, are the digits in a number that represent the precision or accuracy of the measurement. They include all the certain digits plus one uncertain or estimated digit.

How do I determine the number of significant digits in a number?

To determine the number of significant digits in a number, start counting from the first non-zero digit on the left. All non-zero digits are significant. Zeros between non-zero digits are also significant. Zeros at the end of a decimal number are significant. Zeros at the beginning of a decimal number are not significant.

Why is it important to use the correct number of significant digits?

Using the correct number of significant digits is important because it ensures the accuracy and precision of your measurements. Including too many or too few significant digits can lead to incorrect calculations and results.

How do I round a number to the correct number of significant digits?

To round a number to the correct number of significant digits, start by identifying the last significant digit. If the digit to the right of it is 5 or greater, round the last significant digit up by 1. If it is less than 5, leave the last significant digit as is. All digits to the right of the last significant digit should be dropped.

What should I do if I am unsure about the number of significant digits in my measurement?

If you are unsure about the number of significant digits in your measurement, it is best to err on the side of caution and use the minimum number of significant digits. This will ensure that your measurement is not overestimated or underestimated.

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