This explaination compliments of Wikipedia, the Free Encyclopedia:
"Sensors (CCD / CMOS) are often referred to with an imperial fraction designation such as 1/1.8" or 2/3", this measurement actually originates back in the 1950s and the time of Vidicon tubes. Compact digital cameras and Digicams typically have much smaller sensors than a Digital SLR and are thus less sensitive to light and inherently more prone to noise."
For more information, and a complete answer to your question, follow this link:
1/2" means the diagonal of the CCD sensor measures 8mm.1" corresponds 16mm. With fractions, it is usually rouded off to nearest integer. eg., 2/3" corresponds to the diagonal of 11mm, instead of 16*2/3~10.66mm ( see, for example,application note of Edmund Optics).However, this size of sensor alone can not tell vertical and horizontal dimensions of sensor.To know vertical and horizontal dimensions, one needs to know aspect ratio too, which generally is 4:3 (horizontal:vertical) for CCD cameras used industrial/scientific imaging.
Good Answers: