A student rounds 47 + 38 to get an estimate of 90, then calculates an exact answer of 175. What should the student conclude?
AThe estimate was wrong, so the exact answer of 175 must be correct
BThe exact answer is probably wrong — it is far too large compared to the estimate of 90
CBoth answers are reasonable because rounding introduces large errors
DThe estimate should be recalculated to match the exact answer
The estimate of 90 flags that the exact answer should be close to 90. An answer of 175 is nearly double the estimate — that is a huge discrepancy, not a small rounding error. The student almost certainly made an arithmetic mistake (perhaps adding incorrectly, or writing 47 + 38 as if it were a larger problem). The estimate's job is exactly this: to serve as a check. When the exact answer and the estimate diverge wildly, the exact calculation needs to be redone.
Question 2 Multiple Choice
You have $20 and need to buy three items costing $4.89, $6.15, and $3.75. You need to know if you have enough money. What is the most efficient approach?
ACalculate the exact total: $4.89 + $6.15 + $3.75 = $14.79, then compare to $20
BRound each price up to the nearest dollar and add: $5 + $7 + $4 = $16, which is under $20, so you have enough
CGuess based on experience — grocery items are usually cheap enough
DAdd only the two most expensive items to see if those already exceed $20
Estimation is the right tool when you need a quick answer and precision isn't required — 'Do I have enough?' is exactly that kind of question. Rounding each price up to the nearest dollar (always rounding up when checking if you have enough money) gives $5 + $7 + $4 = $16, which is safely under $20. You don't need the exact total of $14.79 to know you're fine. Using exact calculation (option A) works but is slower and harder mentally than estimation.
Question 3 True / False
Estimation is mainly useful in situations where calculating the exact answer is very difficult or too difficult.
TTrue
FFalse
Answer: False
This is a common misconception. Estimation has two uses: (1) providing a quick approximate answer when precision isn't needed, and (2) checking whether an exact calculation is reasonable — even when you have already computed exactly. The second use is arguably more important: after solving 238 × 47, an estimate of 200 × 50 = 10,000 tells you the exact answer should be in the thousands. If your calculator shows 11,186, that's plausible; if it shows 111,860, something went wrong. Estimation serves as a built-in error detector.
Question 4 True / False
Rounding to the nearest ten gives a closer estimate than rounding to the nearest hundred.
TTrue
FFalse
Answer: True
Rounding to the nearest ten preserves more precision than rounding to the nearest hundred, so the estimate is closer to the exact answer. For example, 247 + 389: rounding to hundreds gives 200 + 400 = 600, while rounding to tens gives 250 + 390 = 640. The exact answer is 636, so the tens estimate (640) is much closer. The tradeoff is that rounding to hundreds is faster. Choosing between the two is a judgment call based on how much precision you need versus how quickly you need the answer.
Question 5 Short Answer
Why is estimation described as a 'built-in accuracy check' for exact calculations?
Think about your answer, then reveal below.
Model answer: Because you can compute an estimate before (or after) solving a problem, then compare it to your exact answer. If the two are close, your calculation is probably right. If they're far apart, something went wrong in the exact calculation. The estimate gives you an independent reference point to judge whether your answer is in the right ballpark, catching errors before you rely on a wrong answer.
Estimation works as a check because rounding introduces only small errors (a few percent) in most cases. So if your estimate and exact answer differ by a small amount, that's expected rounding error. If they differ by a large amount — an order of magnitude, or the wrong sign — that signals a real error in the exact calculation. This is one of the most valuable habits in mathematics: never compute without knowing roughly what the answer should be.