A student rounds 349 to the nearest hundred by looking at the 9 in the ones place and deciding to round up to 400. What error did they make?
A9 is indeed the largest digit, so rounding up to 400 is correct
BWhen rounding to the nearest hundred, you look at the tens digit (4), not the ones digit. Since 4 is in the range 0–4, 349 rounds DOWN to 300
C349 rounds to 400 because it is an odd number
DThe student should have averaged 300 and 400 to get 350
The ones digit is irrelevant when rounding to the nearest hundred. Only the tens digit determines rounding direction, because the tens digit tells you whether the leftover (tens + ones) is above or below the halfway point of 50. In 349, the tens digit is 4, so the leftover (49) is less than 50 — round down to 300. Even though the ones digit is 9, 49 < 50, so the answer stays at 300.
Question 2 Multiple Choice
Which digit do you examine when rounding a number to the nearest hundred?
AThe ones digit, because it shows the smallest unit of the number
BThe tens digit, because it determines whether the leftover amount is above or below the 50-unit halfway point between two hundreds
CThe hundreds digit, because you are rounding to hundreds
DThe largest digit in the number
The tens digit is the decision-maker. It represents the most significant part of the 'leftover' below the hundreds place. A tens digit of 5 or more means the leftover is at least 50 (closer to the next hundred); a tens digit of 4 or less means it's below 50 (closer to the current hundred). The ones digit can add at most 9, which cannot push a 4-tens leftover past 50 (40 + 9 = 49 < 50).
Question 3 True / False
The ones digit is irrelevant when rounding to the nearest hundred — only the tens digit determines which hundred a number rounds to.
TTrue
FFalse
Answer: True
Correct. The tens digit tells you whether the combined leftover (tens + ones) is above or below 50. Even at its maximum, a ones digit of 9 with a tens digit of 4 gives a leftover of 49 — still below 50. So no matter what the ones digit is, a tens digit of 0–4 always means round down and 5–9 always means round up. The ones digit cannot change the outcome.
Question 4 True / False
Rounding 350 to the nearest hundred gives 300, because the hundreds digit is 3.
TTrue
FFalse
Answer: False
The hundreds digit tells you which hundred you are near — it does not determine rounding direction. To round 350, look at the tens digit: it is 5. Since 5 ≥ 5, round UP to 400. The hundreds digit (3) shows your current position; the tens digit (5) tells you which direction to go. Confusing these roles is the most common error when learning to round to hundreds.
Question 5 Short Answer
Explain why the tens digit — not the ones digit — determines which hundred a number rounds to.
Think about your answer, then reveal below.
Model answer: When rounding to the nearest hundred, you are asking whether the leftover (everything below the hundreds place) is closer to 0 or to 100. That leftover ranges from 00 to 99, with 50 as the halfway point. The tens digit determines which side of 50 you are on: a tens digit of 5 or more means the leftover is at least 50 (round up); a tens digit of 4 or less means it is below 50 (round down). The ones digit adds at most 9, which cannot push a 4-tens leftover across the 50 threshold.
This is the same rule used for rounding to the nearest ten, just shifted one place to the left — instead of asking 'is the ones digit ≥ 5?', you ask 'is the tens digit ≥ 5?' The underlying logic is identical: you are looking at the digit that represents the 'halfway point' of the interval you're rounding within.