To calculate the tensile stress using the strain gauge, first determine the change in resistance, which is 0.13 ohms (120.13 - 120). The gauge factor of 2.0 indicates that the relative change in resistance is twice the strain. Therefore, the strain can be calculated as the change in resistance divided by the gauge factor, resulting in a strain of 0.065. Finally, tensile stress can be calculated using the material's modulus of elasticity, applying the formula: tensile stress = modulus of elasticity × strain. This method effectively relates the resistance change to the tensile stress experienced by the steel girder.