From an article on Sensor Size in Wikipedia -- the section explains it pretty well and it relates to the use of video tubes
at the time that digital sensor where being developed - and i quote --https://en.wikipedia.org/wiki/Image_sensor_format
Sensor sizes are expressed in inches notation because at the time of the popularization of digital image sensors they were used to replace video camera tubes. The common 1" circular video camera tubes had a rectangular photo sensitive area about 16mm diagonal, so a digital sensor with a 16 mm diagonal size was a 1" video tube equivalent. The name of a 1" digital sensor should more accurately be read as "one inch video camera tube equivalent" sensor. Current digital image sensor size descriptors are the video camera tube equivalency size, not the actual size of the sensor. For example, a 1" sensor has a diagonal measurement of 16mm.
Sizes are often expressed as a fraction of an inch, with a one in the numerator, and a decimal number in the denominator. For example, 1/2.5 converts to 2/5 as a simple fraction, or 0.4 as a decimal number. This "inch" system brings a result approximately 1.5 times the length of the diagonal of the sensor. This "optical format" measure goes back to the way image sizes of video cameras used until the late 1980s were expressed, referring to the outside diameter of the glass envelope of the video camera tube. David Pogue of The New York Times states that "the actual sensor size is much smaller than what the camera companies publish – about one-third smaller." For example, a camera advertising a 1/2.7" sensor does not have a sensor with a diagonal of 0.37"; instead, the diagonal is closer to 0.26". Instead of "formats", these sensor sizes are often called types, as in "1/2-inch-type CCD."
So for all of you that are trying to figure out what those numbers are like 1inch / four/thrids 1/2.3 and others - it has little to do with compaing it to the frame of a standard 35mm (photograpic still image frame size 24mm x 36mm ). It has to do with how it performed / compared to video tube sensors sizes in the days of tube based video sensors.
I hope it helps. thanks and take care - Mobius One