A student rounds 75 to 70, reasoning that '7 is the tens digit so 75 stays near 70.' What is the error?
AThe student should have looked at the tens digit, not the ones digit
BWhen the ones digit is exactly 5, the convention is to round UP — so 75 rounds to 80, not 70
C75 is exactly halfway, so there is no correct answer
DThe student should have rounded 75 to the nearest hundred instead
The ones digit of 75 is 5. The convention for a ones digit of 5 is always to round UP to the higher ten — this is a human convention, not a mathematical necessity, because 5 sits exactly halfway. So 75 rounds to 80. The tens digit tells you where you are; the ones digit tells you which direction to go. The student confused these roles.
Question 2 Multiple Choice
What does the ones digit '3' in the number 53 tell you when rounding to the nearest ten?
A53 rounds up to 60 because 3 is odd
B53 rounds down to 50 because the ones digit 3 is in the range 0–4
C53 rounds down to 50 because the tens digit is 5
D53 rounds up to 60 because there are 5 tens
The ones digit is the only decision-maker when rounding to the nearest ten. A ones digit of 3 falls in the range 0–4, which means 53 is closer to 50 than to 60 (only 3 steps away from 50, and 7 steps from 60). Options C and D confuse the role of the tens digit — the tens digit tells you which ten you are near, but the ones digit tells you which direction to round.
Question 3 True / False
A number's ones digit — and only the ones digit — determines whether you round up or down when rounding to the nearest ten.
TTrue
FFalse
Answer: True
Correct. When rounding to the nearest ten, the tens digit tells you which two multiples of ten the number falls between, but the ones digit is the sole decision-maker for direction. Ones digits 0–4 → round down (stay at the lower ten); ones digits 5–9 → round up (go to the higher ten). No other digit is consulted.
Question 4 True / False
When a number's ones digit is exactly 5, there is no single correct answer because the number is perfectly halfway between two tens.
TTrue
FFalse
Answer: False
By mathematical convention, a ones digit of 5 always rounds UP to the higher ten. This is a convention — a human decision made for consistency — not a logical necessity, because the number is indeed equidistant. But the rule is fixed: 35 → 40, 45 → 50, 75 → 80. Knowing it is a convention (not a law of nature) helps you remember it without wondering why.
Question 5 Short Answer
Explain how you would use a number line to decide whether 63 rounds to 60 or 70.
Think about your answer, then reveal below.
Model answer: On a number line, mark the multiples of ten: 60 and 70. Place 63 between them. Count the distance: 63 is 3 steps from 60 and 7 steps from 70. Since 63 is closer to 60, it rounds down to 60. This matches the rule: ones digit 3 is in the range 0–4, so round down.
The number line makes the concept visual — rounding asks 'which ten is nearest?' and the answer is literally the shorter distance. The ones digit rule is just a shortcut for what the number line shows directly: ones digits 0–4 place the number in the lower half of the gap (closer to the bottom ten); ones digits 5–9 place it in the upper half (closer or equal to the top ten).