Questions: Rounding to the Nearest Ten and Hundred

Question 1

To round 362 to the nearest hundred, which digit do you examine, and why?

• A. The tens digit (6) — it tells you which half of the 300–400 interval 362 falls in
• B. The ones digit (2) — it tells you the exact distance from the nearest hundred
• C. The hundreds digit (3) — that is the place you are rounding to
• D. Both the ones and tens digits — you need both to determine distance

Answer: (A)

When rounding to the nearest hundred, you look at the tens digit — the digit immediately to the right of the place you are rounding to. The tens digit acts as a dividing line: 0–4 means the number is in the lower half of the interval (closer to the lower hundred), 5–9 means it's in the upper half (closer to the higher hundred). For 362, the tens digit is 6, which is ≥ 5, so round up to 400. Examining the ones digit or the hundreds digit gives you no useful information about which hundred is closest.

Question 2

A student says 'round up means make the number bigger.' Is this always true?

• A. No — 'round up' means increase the rounding digit by 1 and replace digits to the right with zeros; the result is always the higher benchmark, which is larger than the original only if you were already past the midpoint
• B. Yes — rounding always produces a number larger than the original
• C. No — rounding always produces a number smaller than the original
• D. Yes — but only when the digit being examined is odd

Answer: (A)

The term 'round up' refers to increasing the rounding place's digit by 1, not to the absolute result being larger than the original. When you 'round up,' the result is always the higher benchmark (e.g., 362 rounds up to 400, which is larger). But when you 'round down,' the result is the lower benchmark, which is smaller than the original. The confusion arises from the phrase 'round up' sounding like 'make bigger' — but it specifically means move to the upper benchmark, which happens when the number is in the upper half of the interval.

Question 3

Rounding 47 to the nearest ten gives 50 because 47 is closer to 50 than to 40 on a number line.

• T. True
• F. False

Answer: True

47 is 7 units away from 40 and only 3 units away from 50 — it is genuinely closer to 50. The 'look at the ones digit' rule confirms this: ones digit 7 ≥ 5, so round up to 50. The number line view and the digit rule always agree; the number line makes the reason visible, while the digit rule is a quick shortcut.

Question 4

When rounding to the nearest ten, you examine the tens digit to decide whether to round up or down.

• T. True
• F. False

Answer: False

When rounding to the nearest ten, you examine the ones digit — the digit one place to the right of the tens. The ones digit tells you which side of the ten-interval you're on. If it's 0–4, you're closer to the lower ten (round down); if it's 5–9, you're closer to the upper ten (round up). Examining the tens digit is the correct move when rounding to the nearest hundred, not the nearest ten. Confusing these is the most common procedural error in place-value rounding.

Question 5

Why is a number line a more reliable tool for understanding rounding than memorizing the 'if the digit is 5 or more, round up' rule?

Model answer: A number line makes rounding concrete: it shows rounding as a question of physical distance — which benchmark is this number closest to? The digit rule is a shortcut that works because the tens digit (for example) tells you which half of the hundred-interval the number is in, which determines the closer hundred. But students who only memorize the rule sometimes apply it mechanically — examining the wrong digit, or forgetting what 'round up' means. The number line lets you check any answer by asking: is this result actually the closer benchmark? It also makes the special case of ties (e.g., 350 is equidistant from 300 and 400) visible as a genuine ambiguity resolved by convention, rather than a mystery.

Understanding rounding as distance also helps students extend the concept correctly: the same logic applies whether you're rounding to the nearest ten, hundred, thousand, or any other place — always find the two surrounding benchmarks and ask which is closer.