Questions: Estimation and Rounding

Question 1

A student rounds 45 to the nearest ten and gets 40. Is this correct?

• A. Yes — 45 ends in 5, which is closer to the lower ten
• B. No — when the ones digit is 5 or more, the rule is to round up, so 45 rounds to 50
• C. Yes — 45 is only 5 steps from 40, so it rounds down
• D. No — 45 is already a multiple of 5, so it doesn't need rounding

Answer: (B)

The rounding rule: if the ones digit is 5 or greater, round up to the next ten. 45 ends in 5, so it rounds up to 50. The distance confirms it: 45 is exactly 5 steps from 40 and exactly 5 steps from 50 — it is the exact midpoint. The convention breaks this tie in favor of rounding up.

Question 2

You estimate 47 + 26 by rounding to get 50 + 30 = 80. You then compute the exact answer and get 63. What should you conclude?

• A. Your estimate was wrong — 80 is too far from 63 to be useful
• B. There is likely an error in your computation — 63 is surprisingly far from the estimate of about 70-80, signaling a mistake
• C. Estimates and exact answers don't need to match, so both answers are acceptable
• D. You should re-estimate using different rounding before accepting either answer

Answer: (B)

47 + 26 should be close to 50 + 30 = 80 (the actual answer is 73). A computed answer of 63 is noticeably far from this range — that gap is the signal that something went wrong in the computation. Estimation's power is this: it gives you a target zone. If your exact answer lands far outside the estimate, recheck before accepting it. The estimate here correctly flags 63 as suspicious.

Question 3

37 rounds to 40 when rounded to the nearest ten.

• T. True
• F. False

Answer: True

37 ends in 7. Since 7 is greater than or equal to 5, the rule says round up. The next ten above 37 is 40. The distance confirms it: 37 is only 3 away from 40, but 7 away from 30 — 40 is clearly the nearest ten.

Question 4

Estimation gives you a close version of the exact answer, so it can replace computation when precision isn't critical.

• T. True
• F. False

Answer: False

Estimation is a tool for checking reasonableness, not for replacing exact computation. 47 + 26 estimated as 50 + 30 = 80 tells you the answer is 'around 70-80' — the exact answer (73) falls in that range, confirming the computation is reasonable. But if you needed to count exact change or measure precisely, only the exact answer works. Rounding serves a checking purpose, not a replacement purpose.

Question 5

A student rounds 47 to 50 and 26 to 30, estimating 47 + 26 ≈ 80. The exact answer is 73. Has rounding 'failed' the student? Why or why not?

Model answer: No — rounding succeeded at its purpose. The estimate of 80 is close enough to 73 to confirm the computation is in the right range. If the student had computed 93 or 43, the estimate would have flagged the error. Rounding is not meant to produce the exact answer — it is meant to produce a quick sanity check.

Rounding fails only if the estimate is so far off that it cannot catch computation errors. Here, the estimate (80) and exact answer (73) are 7 apart — well within the range of rounding error for two rounded numbers. The estimate correctly told the student to expect an answer around 70-80. That check is the whole purpose of rounding in arithmetic.