Yeah, looks like that Dave guy has it right...(oh wait, he's the head of eevblog !)
You need to maintain some consistent context, meaning that saying '10 volts' needs to be more like:
'10 volts with nothing attached'. Then, response is, you needed to have it in circuit, so that little bit of load will bring your battery output down, slightly, maybe down to 9.7 v, to guess what it might settle at.
Now, am I trippen, or isn't the little end '+' on battery ?
And bigger line is your minus (-). LED runs with current
as the symbol points, battery + goes into LED, and LED points to battery minus (-).
Also looks, maybe, like you've added some real measured voltages, adding up to 8.5 V, but then substituted 'nominal' 9.0 V to get that .5 left over...You shouldn't mix your contexts; use an ACTUAL batt voltage, then subtract the measured 8.5.
Example, might be battery at 8.7 with the 2 components dropping 8.5 V. That way your result would be 0.2 V being dropped through your wires and breadboard. I suppose you could try soldering a little test set, to see if that 0.2 V gets 'better', i.e. lower, but I would tend to just shrug, at 0.2 V, just a judgement call (Whatta ya gonna do?), especially for some novice explorations. The half-volt would start to get my notice.
The stuff you can look up, relates to a circular examination: Going all the way, round, should add up to Zero; or looking separately, your 'load' components reading, should match, (equal) your immediate battery reading...that is, the battery voltage reading when in circuit with that exact load.
For example, you wouldn't want to use your running battery reading you remember from yesterday, or on some other LED, it has to be all measured at one sitting.
For the circuit current draw, simply divide I= V/R where V is measured across resistor.
For more reading, I think try 'Kirkoff's Law', that analizes around a circle. Makes sense, but not sure what a Google search might show.
Oh, and avoid the trap, of overusing the LED forward voltage spec. That is a voltage specification, on paper, and not a good starting point as the forward voltage is more like a 'reaction', to current flow. It's confusing, but you might notice, using nominal LED voltage, as you make plans, you can set your LED current, approximately, to match the spec, like, say, 20 mA (that's a lot, for a higher power LED like in flashlight).
THEN, you can go in, after building, and measure everything; that will give you the exact LED voltage, at the exact current that you've ended up with.
Suppose you tried for 20 mA, and end up reading 19.5 mA, that's pretty good. (Btw, I almost always prefer to read current by way of using the resistor drops, along with ACTUAL ohm reading, of your resistor pair. Two resistors 330 ohms, in parallel maybe would read as '146 ohms' (rather than purely '150').