Do All Numbers Have Unlimited Significant Digits?

[Nellen2222]

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

 

[Borek]

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.

 

[Nellen2222]

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..

 

[Borek]

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).

 

[DeeNos]

The concept of significant digits is important in scientific calculations as it helps to maintain the accuracy and precision of our results. A number has unlimited significant digits if it has an infinite number of digits after the decimal point. In scientific measurements, we typically only use a certain number of significant digits based on the precision of our measuring instruments.

Constants, such as Avogadro's number or the speed of light, have an unlimited number of significant digits because they are exact values that do not rely on measurements. However, when using these constants in calculations, it is important to use the appropriate number of significant digits based on the values being used.

Molar masses and densities, on the other hand, have a limited number of significant digits because they are dependent on measurements. When performing calculations involving these values, it is important to use the same number of significant digits as the least precise value being used.

In general, when doing math with numbers, it is important to follow the rules of significant digits to ensure the accuracy and precision of our results. This includes rounding the final answer to the appropriate number of significant digits based on the values used in the calculation.