A student rounds 2.449 to the nearest tenth by first rounding to 2.45 (the 9 rounds up), then rounding 2.45 to 2.5. Their answer is 2.5. What is wrong?
ANothing — 2.5 is the correct answer when rounding 2.449 to the nearest tenth
BRounding should always be done right to left, not left to right
CRounding twice is wrong — look only at the hundredths digit (4), which gives 2.4
DThe student should look at all digits after the tenths place and average them
Rounding is a single-step operation: identify the target place (tenths = 4), look one digit to the right (hundredths = 4), and since 4 < 5, keep the tenths digit as 4. Answer: 2.4. Rounding twice is the most common error — the student lets the distant 9 'cascade' through successive roundings to change the answer. The rule is absolute: look only at the single digit directly after the target place.
Question 2 Multiple Choice
What is 4.862 rounded to the nearest tenth?
A4.8 — the tenths digit is 8, so keep it
B4.9 — the hundredths digit is 6, which is ≥ 5, so round the tenths digit up from 8 to 9
C4.86 — keep two decimal places
D5.0 — round up to the nearest whole number
Target place: tenths (digit = 8). Look one place right: hundredths digit = 6. Since 6 ≥ 5, round up the tenths digit: 8 becomes 9. Result: 4.9. The trap answers are 4.8 (rounding down when you shouldn't) and 4.86 (not actually rounding — just truncating at two places). Option D over-rounds to the whole number place, which wasn't asked.
Question 3 True / False
To round 3.7453 to the nearest hundredth, you look at the thousandths digit (5) and round up, giving 3.75.
TTrue
FFalse
Answer: True
Target place: hundredths (digit = 4). Look one place right: thousandths digit = 5. Since 5 ≥ 5, round up the hundredths digit from 4 to 5. Result: 3.75. This is the rule applied correctly — the thousandths digit (5) is the single digit examined, it meets the threshold, and the hundredths digit increments by 1. The digits beyond thousandths (the 3) are irrelevant.
Question 4 True / False
Rounding 6.95 to the nearest tenth gives 6.9, because 9 is already the digit in the tenths place so you keep it.
TTrue
FFalse
Answer: False
The digit in the tenths place (9) is what you're rounding — don't look at it to decide whether to round, look at the digit after it. The hundredths digit is 5. Since 5 ≥ 5, you round UP the tenths digit: 9 + 1 = 10. That carries over, so the tenths become 0 and the ones digit increases: 6.95 rounds to 7.0. This carry-over case trips up many students because it changes more than just the tenths digit.
Question 5 Short Answer
A classmate rounds 5.349 to the nearest tenth by first rounding to 5.35, then to 5.4. Explain why this is wrong and give the correct answer.
Think about your answer, then reveal below.
Model answer: The classmate rounded twice — this is the cascade error. The correct procedure is to look at only the single digit immediately after the tenths place. The tenths digit is 3; look one place right to the hundredths digit, which is 4. Since 4 < 5, keep the tenths digit as 3 and drop everything after it. The correct answer is 5.3. The 9 in the thousandths place is never consulted — it does not matter.
Cascading roundings compound errors. The first round (to 5.35) incorrectly elevated the hundredths digit from 4 to 5; then the second round used that inflated digit to push the tenths up. Each rounding step introduces distortion — real rounding is always one look to the right of the target, full stop. This is why the rule 'look only at the digit directly after the target place' exists as an absolute.