If one rounds digits one by one starting from the end, then is the rounding same as when "cut-offing" around required the precision?

Question

If one rounds digits one by one starting from the end, then is the rounding same as when "cut-offing" around required the precision?

That is does (for $1/10^3$):

$0.84562...4356 \rightarrow 0.8456 \rightarrow 0.846$

produce the same as

$0.84562...4356 \rightarrow 0.84562...436$
$ \rightarrow 0.84562...44 \rightarrow 0.84562...4$
up until: $\rightarrow 0.846$

Answer 1

No, you cant't use these methods equivalently.

For example by the sequence of rounding we have: $$.846 \approx .85 \approx .9$$ while the single rounding (which is the proper method) gives us: $$.846 \approx .8$$