Uncertainty in parenthesis

Question

In a physics text book I read the following:

$$e/m=1.758820150(44) ×10^{11} mathrm{C/kg} $$ 
  In this expression, $(44)$ indicates the likely uncertainty in the last two digits, $50$.

How should I understand this uncertainty? Does it mean $pm 44$ on the last two digits?

sas · Accepted Answer

The digits in parentheses are the uncertainty, to the precision of the same number of least significant digits. (The meaning of the uncertainty is context-dependent but generally represents a standard deviation, or a 95% confidence interval.) So:
$$e/m=1.758,820,1color{blue}{50},color{magenta}{(44)}×10^{11}  mathrm{C/kg}=left(1.758,820,1color{blue}{50}×10^{11} pm 0.000,000,0color{magenta}{44}×10^{11}right)  mathrm{C/kg}$$

servabat · Answer

The uncertainty is equal to the standard deviation $sigma = 0.000000044×10^{11} C/kg = 4400 C/kg$.  It means you are

approx. 68% confident that the true value $m_e$ lies within the interval $[hat m_e-sigma, hat m_e+sigma]$, where $hat m_e$ is the measure value.
and approx. $95%$ confident that the true value $m_e$ lies within the interval
$[hat m_e-2sigma, hat m_e+2sigma]$.

Uncertainty in parenthesis

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