Are you not supposed consider sig digs for mass?

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In summary, the book gives let statements that always have significant digits. However, it never seems to take mass into consideration. For example, if everything in the question has 3 sig digs and the mass is 2000kg, the final answer will have 3 sig digs. If everything in the question has 3 sig digs and the mass is 250kg, the final answer will still have 3 sig digs. I'm a little confused as to why there is an "exception'. I thought you were supposed to use the lowest number of significant digits given in the question for your final statements.
  • #1
EgpYo
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The answers section in my book gives let statements that always have significant digits. However, it never seems to take mass into consideration. For example, if everything in the question has 3 sig digs and the mass is 2000kg, the final answer will have 3 sig digs. If everything in the question has 3 sig digs and the mass is 250kg, the final answer will still have 3 sig digs. I'm a little confused as to why there is an "exception'. I thought you were supposed to use the lowest number of significant digits given in the question for your final statements. Is my book wrong or is there a reason for this?

Also, do degrees have any affect on significant digits?
 
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  • #2
EgpYo said:
Also, do degrees have any affect on significant digits?
EgpYo said:
3 sig digs and the mass is 2000kg
"2000" has four significant figures; 2.00 x 103 would be three; 2.0 two.
EgpYo said:
3 sig digs and the mass is 250kg
Same game.

EgpYo said:
Also, do degrees have any affect on significant digits?
Angular measure? Temperature? Trig. functions of angular measure?
 
  • #3
I don't understand that then. I thought "2000" would have one significant digit? Are you saying that because 2000 is the equivalent to 2.00x10^3 that it can be considered as having more than one sig dig?

I mean if the questions says something like: "Object is moving 14.0m/s at an angle 7 degrees above the horizontal. Would the final answer have 3 or 1 significant figures?
 
  • #4
And I remember a different example. The minimum number of sig digs given in the question was 3, and the object had a mass of 1.5kg. Final answer was given with 3 significant figures, which doesn't make sense to me.
 
  • #5
First sig. fig. is "2." Second is "0." Third is the second "0." Fourth is the third "0." If you're given 2.00 x 103, you have only the "2" and two zeroes.
EgpYo said:
I thought "2000"

EgpYo said:
14.0m/s at an angle 7 degrees
If the direction is in some way involved in calculations, yes. If it's so much window dressing, no.
 
  • #6
EgpYo said:
1.5kg. Final answer was given with 3 significant figures, which doesn't make sense to me.
That is not a correct statement of significant figures; only two are given, and only two can be reported at the end of the calculation.
 
  • #7
Zeroes can be both significant and not significant. If they say the mass is 2000 kg with 3 significant digits, it can be 2001 kg or 2002.5 kg... it is rounded to the tens. But correctly it should be written as 2.00 x 103 kg.
1.5 kg is given with 2 significant digits. If you want to give it with 3 significant figures you should write 1.50 kg.
 
  • #8

  • Zeros at the end of a number but to the left of a decimal are significant if they have been measured or are the first estimated digit; otherwise, they are not significant. (example: 2000 has just 1 significant digit)
 
  • #9
EgpYo said:
if they have been measured
It's all up to you what you want to call measured or unmeasured. Life is much easier if you get used to certain "conventions" surrounding use of the concept.
 
  • #10
EgpYo said:
Zeros at the end of a number but to the left of a decimal are significant if they have been measured or are the first estimated digit; otherwise, they are not significant. (example: 2000 has just 1 significant digit)
That's a very poor example. The number of significant figures in 2000 is ambiguous since you don't know if the 0s are significant or merely placeholders. The use of scientific notation removes this ambiguity, and that's one reason for using it.

Keep in mind that using the lowest number of sig figs is only a rule of thumb. You can sometimes keep more digits sometimes. For example, 0.99 m + 0.01 m = 1.00 m — if the two measurements are to the nearest centimeter, adding them isn't suddenly going to cause the uncertainty to jump to the nearest decimeter. Similarly, (3.2 m)π = 10.1 m. To figure out the proper number of digits to keep, you'd really have to do error analysis.
 
  • #11
EgpYo said:
I mean if the questions says something like: "Object is moving 14.0m/s at an angle 7 degrees above the horizontal. Would the final answer have 3 or 1 significant figures?
There are calculations where the concept of significant figures does not work any more, and a better error analysis becomes necessary.
For example, the horizontal velocity here is 14.0m/s * cos(7°) = 13.9m/s. You can give three significant figures as the answer does not depend much on the angle, 8° and 6° still lead to the same answer.
 

1. What are significant digits and why are they important in measuring mass?

Significant digits, also known as significant figures, represent the precision or accuracy of a measurement. They are important in measuring mass because they help ensure that the measured value is as accurate and reliable as possible.

2. How do I determine the number of significant digits for a mass measurement?

The general rule for determining significant digits is to count all non-zero digits and any zeros between them. Trailing zeros after a decimal point are also considered significant. For example, 12.03 g has four significant digits.

3. Can I round off significant digits when measuring mass?

Yes, rounding off significant digits is often necessary to express a measurement in a more concise form. However, it is important to follow rounding rules to ensure the accuracy of the measurement. For example, if the last significant digit is 5 or above, the preceding digit should be rounded up. If it is below 5, the preceding digit should be left unchanged.

4. Do I need to consider the units when counting significant digits for mass?

Yes, the units should also be taken into consideration when counting significant digits. The number of significant digits in a measurement should match the number of significant digits in the unit. For example, if a mass is measured to be 12.5 grams, there are three significant digits in both the number and the unit.

5. Why is it important to be consistent with significant digits when performing calculations involving mass?

Using the correct number of significant digits in calculations is important because it ensures that the final result is not more precise than the original measurements. Inconsistent use of significant digits can lead to errors and inaccuracies in the final result.

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