Square root of 3 billion digits. The fraction (…) for the square root of three can be used as an approximation. Despite having a denominator of only 56, it differs from the correct value by less than (approximately ). The rounded value of 1.732 is correct to within 0.01% of the actual value. Archimedes reported , accurate to (six decimal places) and (four decimal places), respectively. It can be expressed as the continued fraction , expanded on the right. It can also be expressed by generalized continued fractions such as which is evaluated at every second term. The following nested square expressions converge to
Root mean square in the frequency domain: If formula_25 is the arithmetic mean and formula_26 is the standard deviation of a population or a waveform then: From this it is clear that the RMS value is always greater than or equal to the average, in that the RMS includes the "error" / square deviation as well. Physical scientists often use the term "root mean square" as a synonym for standard deviation when it can be assumed the input signal has zero mean, i.e., referring to the square root of the mean squared deviation of a signal from a given baseline or fit. This