A student is rounding 95 to the nearest ten. She reasons: 'the tens digit is 9, so I keep the tens digit and change the ones digit to 0 — the answer is 90.' What is wrong with this reasoning?
ANothing — 90 is the correct answer
BShe should round to 100 because the ones digit is 5, so she rounds up, which carries into the hundreds place
CShe should always round to the lower ten when the tens digit is 9
D95 cannot be rounded because it ends in 5
Rounding means finding the closest multiple of 10. On a number line, 95 sits exactly halfway between 90 and 100. By convention, when a number is exactly halfway, we round up — so 95 rounds to 100. Mechanically: the ones digit is 5, so round up. 'Rounding up' from 95 means the ones digit becomes 0 and the tens digit increases by 1 — but 9 tens + 1 = 10 tens, which carries into the hundreds place, giving 100. The tens digit does change in this case.
Question 2 Multiple Choice
A student rounds every number in this list to the nearest ten: 23, 45, 78, 51, 95. Which numbers round to 50?
A45 only
B45 and 51
C45, 51, and 23
D51 only
45 rounds up to 50 (ones digit is 5, round up). 51 rounds down to 50 (ones digit is 1, less than 5, so round down to the lower ten, which is 50). 23 rounds to 20 (ones digit 3, round down). 78 rounds to 80 (ones digit 8, round up). 95 rounds to 100 (ones digit 5, round up — carries into hundreds). So both 45 and 51 round to 50.
Question 3 True / False
The rule 'if the ones digit is 5 or more, round up' is just a trick teachers invented — it has no mathematical reason behind it.
TTrue
FFalse
Answer: False
The rule follows directly from measuring distance on the number line. Any number with a ones digit of 5–9 is at least halfway from the lower ten to the upper ten, meaning the upper ten is as close or closer. The ones digit tells you exactly how far you've traveled past the lower ten: a ones digit of 5 means exactly halfway (round up by convention); 6–9 means past halfway (upper ten is closer). The rule is a shortcut for this distance logic, not an arbitrary convention.
Question 4 True / False
47 is closer to 50 than to 40 on the number line.
TTrue
FFalse
Answer: True
47 is 7 units above 40 and only 3 units below 50. Since 3 < 7, 47 is closer to 50 — so it rounds up to 50. The ones digit of 7 confirms this: any ones digit of 5 or more means the number is at least halfway to the upper ten, so the upper ten is closer.
Question 5 Short Answer
Why does looking at the ones digit tell you which ten to round to?
Think about your answer, then reveal below.
Model answer: The ones digit tells you how far the number has traveled past the lower ten. If the ones digit is 0–4, you haven't reached the halfway point (5), so the lower ten is closer and you round down. If the ones digit is 5–9, you're at or past the halfway point, so the upper ten is as close or closer and you round up. The ones digit is a shortcut for measuring distance between two neighboring tens.
Understanding the ones digit as a distance measure — not just a digit to look up in a rule — is what lets students handle edge cases like 95 correctly. Rather than memorizing exceptions, they can reason: 95 is 5 past 90 and only 5 below 100 — equidistant, so by convention round up to 100.