A successive approximation ADC works by comparing the input voltage to a reference and adjusting its approximation until it matches the input voltage within the quantization error. Given a quantization error of 10 mV, the correct 10-bit output that approximates the input value of 4.365 V corresponds to the binary value \( 0110110100 \), which is the closest to the input voltage in the ADC's resolution. Therefore, the correct answer is option (3).