A question about significant digits of digits in parentheses at the end

  • Thread starter Thread starter swampwiz
  • Start date Start date
  • Tags Tags
    Significant digits
Click For Summary
SUMMARY

The discussion clarifies the representation of Avogadro's number, specifically the notation 6.022 141 29(27)×1023. The digits in parentheses indicate the uncertainty in the last digits of the number, which is ±0.000 000 27×1023. This notation preserves the significant digits while acknowledging the error margin associated with the measurement. Understanding this format is crucial for accurately interpreting scientific constants and their precision.

PREREQUISITES
  • Understanding of significant figures in scientific notation
  • Familiarity with Avogadro's number and its significance in chemistry
  • Basic knowledge of error propagation and measurement uncertainty
  • Proficiency in interpreting scientific data and notation
NEXT STEPS
  • Research the concept of significant figures in scientific measurements
  • Learn about error propagation techniques in experimental data
  • Explore the significance of Avogadro's number in mole calculations
  • Study the conventions of scientific notation and its applications in various fields
USEFUL FOR

Students in chemistry, physicists, and researchers involved in scientific measurements who need to understand the implications of uncertainty in numerical data.

swampwiz
Messages
567
Reaction score
83
I was looking at the value of Avogadro's number

6. 022 141 29(27)×1023

and was trying to figure out what exactly is meant by the parentheses at the end. I'll take a guess and say that the best determined value has these digits, but that the error is high enough so that only by using the number before the parentheses, with its default error of being +/- 1/2 of the value of the last digit place (i.e., here .000 000 01×1023) can the proper number of significant digits be preserved.

Obviously, the most descriptive value would be the one that has the exact amount of uncertainty, but it is not presented here.
 
Physics news on Phys.org
It means 6.022 141 29 * 10^23 +/- 0.000 000 27 * 10^23
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

Similar threads

  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
7
Views
4K
Replies
17
Views
5K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 5 ·
Replies
5
Views
5K
  • · Replies 5 ·
Replies
5
Views
7K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 21 ·
Replies
21
Views
3K