Leo+DadMade for Leo
Rounding Decimals
Rung 3 of 3 · The traps

When Rounding Up Carries

The rule is easy until a 9 gets in the way. That's where marks go missing — the carry, the disappearing zero, and the sneaky double-round.


ExplorePick a sneaky number, hit “round it”, and watch the carry ripple through.
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Most rounding is calm. The trouble starts when the digit you're rounding up is already a 9 — because 9 can't just "go up by one" and stay a single digit. It has to carry.

The Carry

Round 9.96 to 1 decimal place. The kept place is the tenths (the 9), the decider is 6, so round up. But the tenths digit is already 9 — bumping it up makes ten tenths, which is a whole one. So it rolls over: the tenths become 0 and the whole number 9 ticks up to 10. The answer is 10.0, not 9.10 or 10. It works exactly like carrying a column in addition — when a place fills up, the overflow moves left.

Say it plainly: when you round a 9 up, it can't stay a 9 — it becomes a 0 and pushes a 1 into the next place left. Just a carry, same as in addition.

Keep the Trailing Zero

9.96 to 1 dp is 10.0 — and that final 0 is not optional. Writing just "10" claims you rounded to the nearest whole; the .0 is the proof you rounded to a tenth. Trailing zeros after the decimal point carry information: they show the level of accuracy. Drop them and you've quietly changed what your answer means.

Never Double-round

Press 2.349 in the toy. It's tempting to round to 2 dp first (2.349 → 2.35) and then to 1 dp (2.35 → 2.4). That's wrong. Always round once, straight from the original number. Rounding 2.349 to 1 dp: the decider is the very next digit, 4, which is less than 5, so it stays 2.3. Double-rounding let an early bump-up shove the answer the wrong way. One number in, one round, one answer out.

Us, Thinking Out Loud

Why is "10.0" honest but plain "10" misleading after rounding to a tenth?

Can you cook up a number where double-rounding gives the wrong answer?