Questions: Rounding to the Nearest Hundred

Question 1

A student wants to round 463 to the nearest hundred. Which digit should they examine to make this decision?

• A. The tens digit (6)
• B. The ones digit (3)
• C. The hundreds digit (4)
• D. Both the ones and tens digits

Answer: (A)

When rounding to the nearest hundred, you examine the tens digit. The tens digit tells you which half of the hundred-interval the number falls in: tens digit 0–4 means the number is closer to the lower hundred, tens digit 5–9 means it's closer to the upper hundred. The ones digit is irrelevant for this decision. A very common error is examining the ones digit (as you would when rounding to the nearest ten) — in this case, that would give a wrong answer of 460 instead of 500.

Question 2

A student rounds 350 to the nearest hundred. She says '300, because 50 is exactly in the middle — I'll round down to be safe.' What is the correct answer?

• A. 400 — the convention is to round up when the tens digit is exactly 5
• B. 300 — she is right that 50 is in the middle, so either answer is acceptable
• C. 350 — numbers exactly in the middle should not be rounded
• D. 400 — but only because the ones digit is 0

Answer: (A)

The standard rounding convention is: when the deciding digit is exactly 5, round up. So 350 rounds to 400, not 300. The student's reasoning ('in the middle so round down') reflects a natural instinct to be conservative, but it contradicts the mathematical convention. This convention exists so that rounding is consistent and predictable — 'round half up' is the standard rule taught at this level. The ones digit (option D) is not relevant to this decision.

Question 3

When rounding 950 to the nearest hundred, the correct answer is 1,000, even though it crosses into a four-digit number.

• T. True
• F. False

Answer: True

950 has a tens digit of 5, which means round up — increasing the hundreds digit by 1. The hundreds digit of 9 becomes 10, which carries over: 950 rounds to 1,000. This surprises many students who expect the answer to stay a three-digit number, but 1,000 is genuinely the closest multiple of 100 to 950. The number line confirms it: 950 is 50 away from 900 and 50 away from 1,000, and by convention ties round up.

Question 4

To round a number to the nearest hundred, you examine the ones digit.

• T. True
• F. False

Answer: False

To round to the nearest hundred, you examine the tens digit — the digit one place to the right of hundreds. Looking at the ones digit is the correct procedure when rounding to the nearest ten, not the nearest hundred. Each rounding level requires examining the digit immediately to the right of the target place: ones digit for rounding to tens, tens digit for rounding to hundreds. Confusing these levels is the most common error in place-value rounding.

Question 5

A student rounds 847 by looking at the ones digit (7) and concludes the answer is 900. What mistake did they make, and what is the correct process?

Model answer: The student looked at the ones digit instead of the tens digit. When rounding to the nearest hundred, the relevant digit is the tens digit, which tells you which half of the hundred-interval the number occupies. For 847, the tens digit is 4 (not 7). Since 4 < 5, the number is in the lower half of the 800–900 interval, so it rounds down to 800. The correct answer is 800, not 900. The procedure: identify the hundreds digit (8), look one place to the right (tens digit = 4), apply the rule (4 < 5, so keep the hundreds digit and write zeros), giving 800.

This error often comes from students applying the rule mechanically without tracking which place they are examining. A number line check (is 847 closer to 800 or 900?) confirms 800, since 847 is only 47 away from 800 but 53 away from 900.