To round to the nearest ten, look at the ones digit: if 5 or more, round up; if less than 5, round down. To round to the nearest hundred, look at the tens digit. Number lines help visualize rounding.
Use number lines to see which ten or hundred is closest. Practice with many examples.
Using wrong rules; confusing 'round up' with 'make larger'; not understanding rounding's purpose.
Rounding is a way of replacing an exact number with a nearby, simpler number. You already understand place value for three-digit numbers — that gives you exactly the tool you need. Rounding to the nearest ten means finding the closest multiple of 10. Rounding to the nearest hundred means finding the closest multiple of 100. The goal is always the same: which "round" number is this closest to?
A number line makes rounding visual. To round 47 to the nearest ten, place it on a number line between 40 and 50. Is 47 closer to 40 or to 50? It's 7 away from 40 and only 3 away from 50, so it rounds to 50. To round 43, place it between 40 and 50 — it's 3 away from 40 and 7 away from 50, so it rounds to 40. The number line reveals that rounding is really about distance, not about following a rule blindly.
The standard rule — "look at the digit to the right of the place you're rounding to" — is a shortcut for the distance question. When rounding to the nearest ten, look at the ones digit. If it's 0–4, the number is closer to the lower ten, so round down. If it's 5–9, the number is closer (or tied) to the upper ten, so round up. When rounding to the nearest hundred, look at the tens digit the same way. For example, to round 362 to the nearest hundred: the tens digit is 6, which is ≥ 5, so round up to 400.
"Round up" means increase the target digit by one and replace all digits to the right with zeros — it doesn't always make the number larger in an absolute sense, but it moves toward the higher benchmark. "Round down" means keep the target digit the same and replace digits to the right with zeros. Rounding is useful whenever you need an estimate rather than an exact answer: about how many students are in the school? About how far is the drive? Estimation with rounded numbers lets you do quick mental math and check whether exact answers are in the right ballpark.