Final answer:
The round gauge on the blood pressure cuff used to measure blood pressure is called a sphygmomanometer, displaying both systolic and diastolic pressures.
Step-by-step explanation:
The round gauge on the blood pressure cuff is known as a sphygmomanometer, which is a critical medical instrument used to measure blood pressure. It consists of an inflatable cuff that occludes blood flow, a manometer to gauge pressure, and, in manual versions, a stethoscope used to listen for the sound of blood flow. The device displays blood pressure readings, with the higher number representing systolic pressure and the lower number being diastolic pressure. These measurements are essential for diagnosing and monitoring hypertension and other cardiovascular conditions.