The 900mm hand-rail measurement must be taken from the pitch line, which is the line created by the tip of each step/tread. If you put a spirit level or straight piece of timber on top of the treads so it just touches the tip of each nosing (rounded off part) then the bottom edge of the level will be the pitch line. I normally put a level on the treads and transfer the line onto the post, measure up 910mm to be safe and square it round to the front of the post where the hand rail will fall. That mark is the top edge of the handrail.

The easiest way to do this is set a bevel to the angle of your stairs and then cut this angle onto your handrail. Take the offcut and hold it up to the 910mm mark from step 1 above. Now you can mark the underside of the hand rail groove onto the post, which will give you the length a spindle needs to be up from the base rail. Next, cut the same angle onto the bottom of a spindle. Put the spindle into the base rail up against the post and transfer the length onto it. Now you can cut a spindle to the right length to hold the handrail at 910mm, cut an extra one and clamp one to each post - top and bottom. Once these are clamped you have two spindles to rest your hand rail on whilst you are fitting it into position and when you fix it to the posts.

If you divide by 112mm and arrive at 16.07 you must round that number up, so you in fact need 17 spindles. Cut them all exactly the same as the two in step 2 and place all the spindles in the bottom. Measure the remaining space horizontally, and then divide that measurement by 18 (if you have 17 spindles there will be 18 gaps). That will give you the horizontal distance less than 100mm between each spindle. This is not the length of the infill to cut though, you must glue and pin a spindle this distance away from the newel post then cut the angle on the infill and hold it in position and mark it's length. Cut a few of them and try them before cutting enough to get past halfway. There is a step-by-step spindle installation guide at the spindle spacing page and loads more help installing handrails here.

Hope that helps!