# Accuracy and Error of Atomic Clocks

I'm quoting a passage from my notes:

The development of clocks based on atomic oscillations allowed measures of timing with accuracy on the order of $1$ part in $10^{14}$, corresponding to errors of less than one microsecond (one millionth of a second) per year.

I do not understand what the accuracy of $1$ part in $10^{14}$ means. Does it mean that the atomic clocks can tell us the time accurate and ceratain to $10^{-14}s$? How should I understand this? Moreover, what is meant by the error of one microsecond per year? Is it a kind of uncertainty in measurement? How should I understand it? I googled this topic and found information about the atomic clocks and also reviewed the definitions of accuracy and error; however, I'm not able to make any sensisble connection between the concepts. Please help me, thank you.

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It means that if the clock begins set to the correct time, then after time $t$ the clock will be wrong by no more that $(\pm 10^{-14}) t$.

Or as a physicist would be likely put it $$\frac{\delta t}{t} \le 10^{-14} \,.$$

This kind of expression of "fractional errors" is very common in many fields of quantitative science.

Now, to be concrete, a year is about $3.156 \times 10^7 \,\mathrm{s}$, so after one year the clock will be wrong by no more that $$(3.156 \times 10^7 \,\mathrm{s}) \cdot 10^{-14} = 3.156 \times 10^{-7} \,\mathrm{s} = 0.3156 \,\mathrm{\mu s} \,.$$

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