To round a number means to replace it with the nearest round number. You always have to pick first: are you rounding to the nearest ten, hundred, thousand, ten-thousand or hundred-thousand?
The rule: look at the digit just to the right
Follow three steps:
Mark the place you are rounding to (tens, hundreds, thousands, …).
Look at the digit one place to the right.
If that digit is 0–4, round down (keep the marked digit as it is).
If it is 5–9, round up (add 1 to the marked digit).
Replace every digit to the right of the marked place with zeros.
Rounding to the nearest ten
Look at the ones digit and decide.
3 472 → 3 470 (ones 2 < 5, down)
3 478 → 3 480 (ones 8 ≥ 5, up)
3 475 → 3 480 (ones 5, up)
Rounding to the nearest hundred
Look at the tens digit.
3 472 → 3 500 (tens 7 ≥ 5, up)
3 437 → 3 400 (tens 3 < 5, down)
6 950 → 7 000 (tens 5, up — 9 hundreds becomes 10 hundreds, which carries into the thousands!)
💡 When the digit you bump up "overflows" past 9, the carry rolls into the next place. 6 950 rounded up at the hundreds place is 6 (9+1) hundreds = 7 thousands = 7 000.
Rounding to the nearest thousand
Look at the hundreds digit.
3 472 → 3 000 (hundreds 4 < 5, down)
3 572 → 4 000 (hundreds 5, up)
9 800 → 10 000 (hundreds 8, up — again the carry rolls over)
Rounding to ten-thousand and hundred-thousand
The same rule keeps working, you just look further left.
285 472 → 290 000 (rounding to the nearest 10 000; look at thousands 5, up)
285 472 → 300 000 (rounding to the nearest 100 000; look at ten-thousands 8, up)
285 472 → 285 470 (rounding to the nearest 10; look at ones 2, down)
A picture: half-way on the number line
Imagine the number line. 3 472 sits between 3 400 and 3 500. Which is closer?
3 400 ←—— 3 472 ——— 3 500
Distance from 3 472 to 3 400 is 72.
Distance from 3 472 to 3 500 is 28.
3 500 is closer, so we round up. That's exactly what the rule does — faster, because you only need to peek at the next digit.
