rounding
/ ROWND-ing /
When a cashier tells you the change is 'about three dollars' instead of $2.9847, they are rounding — trimming a number down to a tidy, honest length by dropping digits you don't need. In the lab, rounding is how you cut a calculated result back to only the digits you can actually justify, so the number you report doesn't pretend to be more precise than your measurement allows.
Rounding replaces a number with a nearby value having fewer digits, following a rule. The familiar rule: look at the first digit you are dropping — if it is less than 5, round down (leave the kept digit alone); if it is more than 5, round up. The subtle case is exactly 5 with nothing after it, where the common scientific convention is 'round half to even' (round to the nearest even digit), which avoids a slight upward bias that always-rounding-up would create over many numbers.
Rounding matters because reporting a result with the right number of digits is part of telling the truth about your data — too many digits is a quiet lie about precision. The crucial caveat, drilled into every analyst: round only the final answer, never the intermediate steps. Rounding partway through a calculation discards information and lets small errors accumulate, so you carry extra guard digits all the way and round just once at the end.
Rounding 0.2485 to three significant figures gives 0.248 by the round-half-to-even rule, because the digit kept (8) is already even; but 0.2475 rounds to 0.248 as well, since 7 must go up to the nearest even, 8.
Round-half-to-even avoids a built-in upward drift.
If the digit after the 5 is anything other than nothing (e.g. 0.24851), you always round up regardless of even/odd — the even rule only settles the exact-half tie.