How do you round numbers so that it affects computation?

Just specify the nearest multiple in the second argument.

Round[123.456, 0.01]

123.46

Suppose Round did not take a second argument as it does. What to do?

myround[n_, a_] := Round[n/a] a

myround[π, 0.001]

myround[π, 1/7]

3.142

22/7

round1[x_, n_] := Ceiling[10^n x]/10^n // N
round2[x_, n_] := Floor[10^n x]/10^n // N
round1[3.4647, 1]
round2[3.4647, 2]

3.5
3.46