AFAIK marcros, a piece of 10 mm dia silver steel should be EXACTLY 10 mm (to within a VERY tight tolerance). I'm not 100% sure mind, but 99%, and certainly any silver steel I've bought (both from the model engineering suppliers and from a local steel stock holder - where I had to buy 5 Metres length!!!) has always been spot on the quoted diameter. So I THINK something's gone wrong at your supplier and would take/send it back if I were you.
Even buying just plain old MS bar at 10 mm dia will be much nearer 10 mm than your 9.4/10 mm SS.
Macros, I agree with Trevanion it seems you have been sent 3/8" [9.525mm]
Quality silver steel is sold in 13" or now 1m lengths and made to a tolerance of +/- 0.00025" this has been the norm for the last 60 years, it was pretty much PS Stubbs who were the major supplier/producer in Britain but now there are several. I use Coventry Grinders or Ground Flat Stock thus ensuring a known quality product.