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We have investigated noise in measurements of the 10 V outputs of electronic voltage standards based on Zener diode references (Zeners). Zener outputs were compared to NIST Josephson standards using a digital voltmeter (DVM) to measure voltage differences. Because of the presence of serially correlated noise, the data were analyzed by calculating estimated Allan variances which were then used to determine the parameters of a power law model including white and 1/f noise. In many cases, the modeled Allan variances agree well with the estimated values over a wide range of sampling times. In all, we have estimated the 1/f noise floor for 25 Zeners of three types. We examined the impact on noise measurements of changes of the range of the DVM and of quantization of the recorded voltages by the DVM. We conclude that there is strong evidence of the presence of a high level of white noise in Zeners.