# Significant digits question

## 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 dont count it when i do my math, etc?

## The Attempt at a Solution

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Borek
Mentor
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 dont have to worry about that anymore..

Borek
Mentor
In kinetic energy definition - $E_k = \frac{mv^2}{2}$ 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).