what does "(71)" mean in the expression 1.416785(71) x 10^32?

[PG1995]

Hi

I was reading **broken link removed** Wikipedia article and there it was written:

Current cosmological models postulate that the highest possible temperature is the Planck temperature, which has the value 1.416785(71)×10^32 kelvin.

What does "(71)" mean? Does it mean that the expression "1.416785" has been computed up to 71 decimal places? Please help me with it. Thank you.

Regards
PG

 

[jpanhalt]

From Wikipedia:

The two digits inside the parentheses denote the standard uncertainty in the last two digits of the value.

John

 

[PG1995]

Thank you, John.

I was also able to the source you have quoted but I still didn't get what it meant. What does it mean in simple words? In other words, I don't get the part where it says the uncertainty in the last two digits of the value. Perhaps, you could use some simple value to help me understand the concept. Thank you

Regards
PG

 

[jpanhalt]

Here: https://physics.nist.gov/cgi-bin/cuu/Value?h|search_for=planck

Click on the definition of standard uncertainty, if it is not clear from the example. You may want to look up the term "standard deviation." (https://en.wikipedia.org/wiki/Standard_deviation)

A useful number to remember is that with a normal distribution of estimates, say numerous unbiased measurements of a fixed voltage, 95% of the measurements will fall within 2 standard deviations of the mean of the measurements. The term "coefficient of variation," which is usually abbreviated as "CV," is often used as a dimensionless representation of the standard deviation. The CV is simply the standard deviation divided by the mean and expressed as a percentage of the mean. Thus, if the mean of a many measurements is 100 and the CV is 5%, one would expect 95% of the measurements to be in the range of 100 ±10, i.e., 90 to 110.

Edit: In other words, given your original post regarding Planck temperature: 1.416785(71) x 10^32 Kelvin. The claim is that the true maximum temperature has a 95% probability of being between 1.416785 x 10^32 ￾±0.000142 x 10^32 Kelvin (i.e., within ±2 standard deviations).

John