Two students round 449 to the nearest hundred. Student A rounds 449 → 450 → 500 (two steps). Student B looks at the tens digit (4) and rounds directly to 400. Which student is correct?
AStudent A — working through smaller place values first is more careful and accurate
BStudent B — look directly at the digit immediately to the right of the target place and ignore everything else
CBoth students are correct; chaining and direct rounding give the same answer
DNeither — 449 rounds to 450 when rounding to the nearest hundred
Student B is correct. To round 449 to the nearest hundred, look only at the tens digit: it is 4. Since 4 < 5, round down to 400. Student A's chaining method gives the wrong answer: first rounding 449 to 450 changes the tens digit from 4 to 5, and then the second step rounds up to 500 — but the original number (449) is closer to 400 than to 500. Chaining corrupts the answer by using a modified digit instead of the original.
Question 2 Multiple Choice
Before computing 5,738 + 2,491, you want to estimate the answer to check your work. What is the best approach?
ACalculate the exact answer first, then round it to estimate
BRound both numbers to the nearest thousand first, then add: 6,000 + 2,000 = 8,000
CRound only the larger number to the nearest thousand: 6,000 + 2,491 ≈ 8,491
DAverage the two numbers and double the result
For a quick estimate, round both numbers to the nearest thousand: 5,738 ≈ 6,000 and 2,491 ≈ 2,000, giving 8,000. This tells you immediately that the exact answer should be close to 8,000. If you get 72,290 on a calculator, you know something went wrong — a calculation error or misplaced digit. Rounding before calculating gives you a sanity-check target; the point of estimation is speed and reasonableness, not precision.
Question 3 True / False
When rounding 3,472 to the nearest hundred, you should consider both the tens digit and the ones digit to decide whether to round up or down.
TTrue
FFalse
Answer: False
Only the digit immediately to the right of the target place matters. To round to the nearest hundred, look at the tens digit only (7 in this case). Since 7 ≥ 5, round up to 3,500. The ones digit (2) is irrelevant — you do not look at it. This single-digit rule is what makes rounding fast. Looking at multiple digits (or chaining) introduces errors rather than accuracy.
Question 4 True / False
Rounding is most useful as a way to check whether a calculated answer is in the right ballpark, rather than as a way to find an exact answer.
TTrue
FFalse
Answer: True
Rounding is an approximation tool, not a precision tool. Its power is in estimation: by quickly rounding numbers before or after a calculation, you can verify that an exact answer is reasonable. If 4,872 + 3,215 is estimated at about 8,000 and your calculator shows 8,087, that's plausible. If it shows 80,870, something went wrong. Estimation via rounding is how mathematicians, engineers, and shoppers sanity-check their arithmetic without needing to recompute everything from scratch.
Question 5 Short Answer
Explain the 'chaining' mistake in rounding and why it gives the wrong answer. What should you do instead?
Think about your answer, then reveal below.
Model answer: Chaining means rounding in multiple steps — for example, rounding 449 to the nearest hundred by first rounding to 450 (nearest ten), then rounding 450 to 500. This is wrong because the second step uses the already-modified number (450) instead of the original (449). The tens digit in 449 is 4, which correctly rounds down to 400. But after chaining to 450, the tens digit is now 5, which rounds up to 500 — the wrong answer. The correct approach: identify the target place, look only at the digit immediately to its right, and round in one step.
Chaining feels more careful but actually introduces error. It modifies a digit before using it to make the rounding decision. The rule is simple and one-step: identify the target place value, look at the single digit to its right, apply the rule (≥5 rounds up, <5 rounds down), and replace all digits to the right of the target place with zeros. One look, one decision.