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We present measurement data of fundamental thermal noise in a 40-m fiber optic Mach-Zehnder interferometer (MZI) using 80-μm-diameter optical fiber. To extend the measurements to low frequencies (below 500 Hz), the experimental setup is carefully designed to minimize ambient noise, thermal drift, and the phase and amplitude noise of the lasers. These experimental results are compared with theoretical predictions for the magnitude of the fundamental thermal noise in fiber, due to both thermodynamic temperature fluctuations and spontaneous length fluctuations. The experimental data, using two different solid-state lasers with two different emission wavelengths (1319 and 1550 nm), is in reasonable agreement with both theories over frequencies ranging from 20 Hz to 100 kHz. In terms of strain resolution, this paper demonstrates a fundamental thermal noise limit of approximately one femtostrain/rt(Hz) for a 40-m fiber optic MZI.