Do All Numbers Have Unlimited Significant Digits?

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Discussion Overview

The discussion revolves around the concept of significant digits in numbers, particularly in the context of constants, molar masses, and densities. Participants explore whether certain numbers can be considered to have unlimited significant digits and how this affects calculations in physics and chemistry.

Discussion Character

  • Homework-related
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions how to determine if a number has unlimited significant digits, specifically asking about constants, molar masses, and densities.
  • Another participant asserts that constants and molar masses do not have unlimited significant digits and emphasizes that significant digits are often presented clearly.
  • A participant mentions that significant digits are not the primary way to express precision, providing an example of the ideal gas constant and its uncertainty notation.
  • Another participant expresses concern about strict grading on significant figures and seeks clarification on how to handle them in calculations.
  • A later reply states that certain numbers, like the definition of kinetic energy and the value of pi, are examples of numbers with unlimited significant digits, while also noting that some coefficients in chemical formulas may have limited precision.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the treatment of significant digits, with differing views on what constitutes unlimited significant digits and how they should be applied in calculations.

Contextual Notes

There are limitations in the discussion regarding the definitions of significant digits and the context in which they are applied, as well as the varying standards for precision in different fields.

Nellen2222
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Homework Statement



How do I know if a number has unlimited significant digits or not? do constants and molar masses and densities all have an unlimited number? does this mean i don't count it when i do my math, etc?


Homework Equations





The Attempt at a Solution

 
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Nellen2222 said:
do constants and molar masses and densities all have an unlimited number?

No. They will be usually given to you in a way that will make number of significant digits clear.

Note that significant digits are not what grown ups use to express precision. For example correct way if expressing precision of the ideal gas constant (J/(K*mol)) as is currently known is 8.3144621(75) - digits in parentheses are uncertainty (standard deviation) of the last two digits of the constant (in other words we know the exact value to be 8.3144621±0.0000075 with probability 0.68, or 8.3144621±3*0.0000075 with probability 0.997).

Bottom line: don't worry too much about sig figs. Learn how to use them, but don't treat them too seriously.
 
Well, My prof marks us hard on them. so.. Uhh yeah. So i treat densities and molar mass etc with proper sig-figs and carry them to the final answer then round at the end right? So what is an example of a number with unlimited sig figs? Since I don't have to worry about that anymore..
 
In kinetic energy definition - [itex]E_k = \frac{mv^2}{2}[/itex] both 2s have unlimited number of sig figs.

Pi has unlimited number of sig figs (even if we will be never able to calculate them all).

In water molecule H2O 2 is an exact number (but there are non stoichiometric compounds where coefficients can be known with a limited precision).
 

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