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1:87 is the scale ratio, which means that a linear measurement of 1 actual unit is equal to 87 times the scale measurement. For example, one real foot equals 87 scale HO feet. But the ratio works for any linear unit of measurement, whether it's inches, meters, millimeters, miles, furlongs, or light-years. (an HO scale light-year is 67.5 billion actual miles long, by the way )
If you're asking how many actual inches are in a scale HO foot, then a little math is involved:
In 1 real foot (ft), there are 87 HO scale ft (HOft).
There are 12 real inches (in) in 1 real foot (ft).
So you multiply 1/87 (ft/HOft) x 12/1 (in/ft), and you get a ratio of 12/87, which equals 0.1379. The "ft" units cancel out, leaving you with inches / HO scale feet. 0.1379 comes out to just shy of 9/64 inches (per scale HO foot).
I would suggest getting an HO Scale Ruler. Mascot made a nice one that was affordable in stainless steel. Mine has HO scale feet, along with S, O, and N. There is also drill & tap information and a metric scale. Since getting into detailing locomotives years ago, the scale ruler has become an important tool on my bench. http://www.walthers.com/exec/search?quick=scale+ruler
I was doing some 3d drafting in 1 to 1 scale. I wanted to reduce to HO scale but used 87 once and 87.1 another time. The parts didn't fit. The most accurate way I came up with is 3.5mm/12in per ft/25.4 mm per inch =.011482 actual inches per inch. Or 1/87.08751. That makes 1 ft =.13779 inches, if you need wire EDM precision.
Nothing good happens trying to mix imperial and metric.
Edit: Just realized this thread is kinda old. The math doesn't change though.
This ruler in HO scale (1:87.1 scale) is great for use by model railroad enthusiasts, doll house builders, and all other hobbyists. Free to download and print