L3 · Estimation: is the answer reasonable?

Learning goal

“I can estimate a sum or difference by rounding both numbers to a sensible place, judge whether a given answer is reasonable, and choose how precise my estimate needs to be for the job.”

Estimate — a quick calculation with rounded numbers that predicts about what an exact answer should be.

Reasonable — an answer is reasonable if it lands close to a good estimate; wildly far answers signal an error somewhere.

Round — to replace a number with a nearby number at a chosen place (recap of G5U01 L4 - the estimation engine).

Exact answer — the precise result of the standard algorithm; the estimate judges it, never replaces it when precision matters.

Worked example

Estimate 48,372 + 21,509. Step 1 (choose the place): the numbers are in the ten-thousands - round to the nearest thousand for a fast, close estimate. Step 2 (round BOTH): 48,372 -> 48,000; 21,509 -> 22,000 (509 is past the halfway 500). Step 3 (compute the estimate): 48,000 + 22,000 = 70,000. Step 4 (compare with exact): the standard algorithm gives 69,881 - 119 away from the estimate. Reasonable. (Notice rounding pushed the estimate slightly HIGH here; an estimate is a neighbourhood, not a verdict - answers within a few hundred of it pass.)

Check yourself — explain it

We round both numbers before estimating because...

Paired problem — example still visible

Estimate 6.84 + 3.27 by rounding to the nearest whole number -> 10 (7 + 3; exact: 10.11)

Faded completion — last step is yours

"Estimate 512,608 - 198,377 to the nearest hundred thousand: 500,000 - 200,000 = ___" -> 300,000 (exact: 314,231)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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