Rounding a decimal works exactly like rounding a whole number: we swap an awkward number for a tidy nearby one. The only new question is how many digits after the point we want to keep — that is the number of decimal places (d.p.).

Here is the whole trick. To round to a given place, look only at the very next digit — the one just after the place you are keeping:

• that next digit is 5 or more → round up;
• that next digit is 4 or less → round down (keep it as is).

Round 3.47 to 1 d.p. We are keeping one digit after the point (the 4). The next digit is 7, which is 5 or more, so we round up:

Round 0.832 to 2 d.p. We keep two digits (the 3); the next digit is 2, which is 4 or less, so we round down and drop it:

Why does “5 or more rounds up” work? Because a decimal sits between two neighbours, and the next digit tells you which half you are in. Rounding to 1 d.p. snaps a number to the nearer tenth — the midpoint between two tenths is the 5 in the next place, and anything from there on is closer to the tenth above.

Press play, then replay it. A two-digit decimal appears between its two tenths; we mark the halfway point, then snap the number to the nearer tenth — that is rounding to 1 decimal place.

Two small things to watch. First, only ever look at the one digit right after your place — never the whole tail. Rounding 0.749 to 1 d.p. gives 0.7, because the next digit is just 4 (the 9 after it does not get a vote).

Second, rounding up can carry. Rounding 2.96 to 1 d.p., the next digit is 6, so the 9 rolls over:

A gentle peek ahead: significant figures (s.f.) count from the first non-zero digit instead of from the decimal point. So 0.00482 to 2 s.f. is 0.0048 — the leading zeros do not count, and the rule is the same: look at the next digit (2 here, so round down). The “5 or more” rule never changes; significant figures just change which digit you are keeping. We will give this its own page later.

Khan Academy rounds decimals to the nearest tenth here: