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The La_{0.7}Sr_{0.3}MnO_{3} perovskite is a ferromagnetic half-metal with a strong spin polarization and high Curie temperature T_{C} (355K). We have shown that a combination of the break junction technique with the special properties of the La_{0.7}Sr_{0.3}MnO_{3} perovskite can lead to extremely high values of tunneling magnetoresistance ratio (> 10^{3}%) and high field sensitivity (30%/Oe). These results are obtained in magnetic fields below 1kOe and at room temperature.