Question about sig figs

  • Thread starter jaydnul
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In summary, significant figures are important in giving accurate and honest answers in calculations. It is best to use more significant figures in intermediate steps and apply the significant figure rules only at the end. The number of significant figures in a final result is determined by the least accurate measurement. Sigfigs are not a universal rule and may vary among different instructors. There are better ways to deal with uncertainties than using significant figures.
  • #1
jaydnul
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Actually multiple questions:
(1) Am i supposed to use the rules of sig figs all the way through a calculation or just for the final answer? If not, how do i know when the proper time to use them is? The reason i ask is because if you have, say, 2/3, the answer is .666666 repeating, but according to the rules of sig figs, its .7, but this isn't as accurate.
(2) When using trig functions, do I use the amount of least sig figs or least decimal places? I would assume sig figs since a trig function is just division.

Thanks
 
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  • #2
lundyjb said:
Actually multiple questions:
(1) Am i supposed to use the rules of sig figs all the way through a calculation or just for the final answer? If not, how do i know when the proper time to use them is? The reason i ask is because if you have, say, 2/3, the answer is .666666 repeating, but according to the rules of sig figs, its .7, but this isn't as accurate.
(2) When using trig functions, do I use the amount of least sig figs or least decimal places? I would assume sig figs since a trig function is just division.

Thanks
The quick answer is you should use more significant figures when working out the intermediate steps in the calculation, then apply your significant figure rule at the very end.

But here a couple of additional points.
  • The significant figure rules are between you and your instructor (e.g., three significant figures, four significant figures, etc). There are not any universal rules regarding this. In the future, you might end up with different significant figure rules. Whatever the case, my advice still applies: use more significant figures in the intermediate steps, and apply the significant figure rules only at the very end.
  • Your example of 2/3 (.666666 repeating) being .7 is only one significant figure (I'm betting your instructor's rules are more than that). The number of significant figures starts after ignoring all leading zeros. So if your rule is three significant figures, 2/3 comes to 0.667. For four significant figures it comes out as 0.6667.
 
  • #3
collinsmark said:
The quick answer is you should use more significant figures when working out the intermediate steps in the calculation

I believe these are technically called guard digits.

Whatever the name is, only the final result gets rounded (unless one wants to report intermediate results - then they should be reported rounded, but not used rounded for calculations).

The significant figure rules are between you and your instructor (e.g., three significant figures, four significant figures, etc). There are not any universal rules regarding this.

Not exactly - there are more or less universal rules about how to determine number of significant digits in the final result, based on the significant digits in the data.

lundyjb said:
The reason i ask is because if you have, say, 2/3, the answer is .666666 repeating, but according to the rules of sig figs, its .7, but this isn't as accurate.

Depending on the context 2/3 can be an exact value, with infinite number of significant digits. You don't round kinetic energy to 1 significant digit just because 2 in [itex]\frac {mv^2}{2}[/itex] is written with one significant digit.

Don't worry too much about sigfigs. There are much better ways of dealing with uncertainties. Sigfigs are just an approximate rule of thumb.
 
  • #4
"Significant figures" are important in giving honest answers. If you measure the distance traveled as 58.67 km in 1.3 hours then you have measured distance to 4 significant figures while time is measured only to 2 significant figures. That means that the distance could be anywhere from 58.665 to 58.675 km and the time could be any where from 1.25 hours to 1.35 hours.

Just dividing 58.67 by 1.3 would give 45.130769230769230769230769230769... "km per hr". A calculation cannot be more accurate than the least accurate measurement so the correct statement would be that the speed was 45 km/hr- it could be any where from 44.5 to 45.5 km/hr. To say any more would imply a more accurate measurement. Writing the speed as 45.1 km/hr would imply that we are sure the speed is between 45.05 and 45.15.
 
  • #5
for your questions about significant figures (sig figs). Sig figs are an important concept in scientific calculations as they help us determine the precision of our measurements and calculations. To answer your first question, you should use the rules of sig figs throughout your calculation, not just for the final answer. This ensures that your final answer is as accurate as possible based on the precision of your measurements. In the example you provided, 2/3 is indeed equal to .666666 repeating, but since 2 and 3 only have one significant figure each, the answer should be rounded to .7. This may not seem as accurate, but it is a more precise representation of the original measurements.

For your second question, when using trig functions, you should use the amount of least sig figs. This is because, as you mentioned, a trig function is just division and the number of sig figs in the original measurements should be maintained. However, if you are using values with different numbers of decimal places, you should use the least number of decimal places in your calculation.

I hope this helps clarify the use of sig figs in scientific calculations. It's important to remember that sig figs are a way to express the precision of our measurements and calculations, and using them correctly can help us avoid errors and make more accurate conclusions. If you have any further questions, please don't hesitate to ask!
 

1. What are significant figures (sig figs)?

Significant figures, also known as significant digits, are numbers that represent the precision of a measurement or calculation. They indicate the reliability of a number and how many digits are considered accurate.

2. How do I determine the number of significant figures in a number?

The general rule for determining significant figures in a number is to count all the non-zero digits and any zeros between them. For example, the number 120.03 has five significant figures, while 0.005 has only one significant figure.

3. What is the significance of using significant figures in scientific measurements?

Using significant figures helps to communicate the accuracy and precision of scientific data. It ensures that calculations and measurements are reported with the appropriate level of precision and avoids misleading others with false levels of accuracy.

4. How do I round a number to the correct number of significant figures?

To round a number to the correct number of significant figures, start from the leftmost non-zero digit and count the digits until you reach the desired number of significant figures. If the next digit is 5 or higher, round up the last significant figure. If it is 4 or lower, leave the last significant figure as it is.

5. Can significant figures be added, subtracted, multiplied, or divided?

Yes, significant figures can be used in calculations. When adding or subtracting, the result should be rounded to the least number of decimal places in the original numbers. When multiplying or dividing, the result should be rounded to the least number of significant figures in the original numbers.

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