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Understanding Amp Hours
I am trying to deterimine how much time I have on my deep cycle which is good for approximately 190 amp hours. Assuming I am running on a 12 volt battery, does a 9 watt electrical device (my GPS) draw 9/12 (or .75) amps per hour? A little EE help would be very much appreciated.

Watts/Volts=Amps

Yep. watts =volts x amps. Your working capacity is down to 50% of battery capacity and probably to about 95% as it is difficult to get full charge, depending on charging system.

So...you essentialy have 95 amp hours to work with and this means your GPS can run for about 150 hours before you should recharge your batteries.
Note that 12.25V measured in RESTING state is 1/2 discharged for a 12V battery. About 12.8V is fully charged. 
Just remember that the amphour level of a battery bank is also dependent on the size of the draw. If the draw is fairly low, the effective amphour rating of the battery bank will be higher than if the load on the bank is high. The higher the load, the lower the effective amphour rating of a battery bank will be.
The GPS is a fairly light load, and will give you a fairly long run time. A 120 Watt 12 VDC searchlight will kill the battery far more quickly, probably bringing you down to the 50% level in 8 hours, rather than the 9.5 hours you would expect. 
If you know your Peukert # for your battery you can use this formula to see how long your battery will last for a particular load. This is kinda technical so stop reading here if ya don't wanna go nuts!
Peukerts Equation: I <sup>n</sup> x T = C The AMPS use (I) to the Peukert # exponent (N) multiplied by time (T) = the battery amp hour capacity (at the 100 hour discharge rate...or 1.1 times the 20 hour capacity) Example...let imagine a 200 a/h battery (at 20 hr. rating) with a typical flooded battery Peukert rating of 1.2 and you want to know how long you can run your 5amp refrigerator. Well 5 amps raised to the 1.2 power is almost 7. The 200 amp at 20 hr battery needs to be raised by 10% to 220 So we have 7(T) =220 or a bit over 31 hours to total discharge of the battery...so figure on 15 hours before you need to recharge. If everything remained the same BUT you changed to a 10 amp fridge... the 10 to the 1.2 is almost 16 and you thus get 16T=220...or 13.5 hours till total discharge and just 67 hours before you need to recharge. So...you can see that as current draw increases...the capacity of the battery in hours drops even more quickly...and a higher Peukert number accelerates this. Now conversely...a low Puekert # means the capacity is relatively unnaffected by the rate of amp draw. This is one of the big advantages of AGM batteries as they can have P numbers in the 1.08 type range. So....if you are looking at building a large battery bank with big amp draws...checking into your PARTICULAR brand and model battery choices Peukert # may lead you to one brand and one type over another. Peukert #'s are generally hard to find and you may need to write to the mfr. you are considering. Hope a few find the above interesting. 
Cam
"Note that 12.25V measured in RESTING state is 1/2 discharged for a 12V battery. About 12.8V is fully charged" SAY WHAT?! The normal resting voltage for a wet lead battery is six cells at 2.2VDC, total 12.6VDC. 12.8V is a "hot" battery with a surface charge on it, or a different internal chemistry. 12.5V is a 90% charged conventional battery, rated from 11.6V to 12.6V for the working range from "dead" to "full", typically and nominally. At least, that's what I keep getting repeatedly from a wide variety of makers and sources. 
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Actually, your math skills suck... 2.2 V x 6 = 12 (6 x 2) + 1.2 (6 x .2) or 13.2 Volts... Did you mean to say that the cells are 2.1 VDC each?? Six cells at 2.1 VDC would be 12.6 VDC total. 
SD
How many times do I have to remind you, I'm not licensed to practice math on the internet?<G> I agree the numbers don't add up. AFAIK they refer to the cells as 2.2V but the battery as 12.6. SO digging out the old GE Wet Lead handbook...you are right, they are nominally rated at 2.1 VDC each cell, with a potential of 2.05 to 2.40 volts while charging, and 2.3 to 2.8V while overcharging and gassing at the terminals. But that's for "pure" Pb or PbO2 versus H2SO4 chemistry, and since most batteries add something else into the lead for a variety of reasons, that's also "just" a textbook battery, probably at a textbook 68F/20C also. GE used to give the book out for free, their part # BBDOEM237, to help people spec installations of GE lead batteries. (You know, I pay you to catch these errors before I post them, not after. You're falling down on the job.) 
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