ROUND 5 up/down according to the next digit

ROUND will round the numbers 1-4 down and 5-9 up.

So, for instance, if I have 4.2253 at cell A1 with the formula =ROUND(A1,2), the result would be 4.2300. However, I want the function to look at the next digit ("3") if the digit that determines the rounding ("5") is 5. So "3" rounds "5" down resulting in 4.2200 instead.

Here are a couple examples of what I mean:

number > result using ROUND with num_digits=2 > result I desire

4.2210 > 4.2200 > 4.2200
4.2260 > 4.2300 > 4.2300
4.2251 > 4.2300 > 4.2200 (logic: if 0.00X is 5 look at 0.000X and round 1-4 down 5-9 up)
4.2256 > 4.2300 > 4.2300 ("6" rounds "5" up to 6 which rounds "2" up to 3)
4.2255 > 4.2300 > 4.2300 ("2nd 5" rounds "1st 5" up to 6 which rounds "2" up to 3)

Is there a formula for this? I've been trying to figure this out for hours lol, please help.