Or if your number is actually character data. 😀
declare @number varchar(20) = '1000000017777'
select @number as before
select @number = RIGHT(@NUMBER,len(@number) - PATINDEX('%0[^0]%',@number))
select @number as After
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Against stupidity the gods themselves contend in vain. -- Friedrich Schiller
Stop, children, what's that sound? Everybody look what's going down. -- Stephen Stills