How to Estimate Answers
Level 2 Rounding and estimation · Reviewed by The NumThink editorial team · Last reviewed
This page is part of the NumThink Rounding and estimation course. Read why the method works, watch it run on worked examples, then drill it in the practice box below until it feels automatic.
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No signup · instant feedbackWhy it works
Rounding to the first digit leaves one non-zero digit in each number, so the calculation becomes a times-table fact plus zeros: 50 × 20 is 5 × 2 = 10 with two more zeros, which is 1,000.
Usually the rounding error is small compared with the answer, so the estimate lands in the right range — and an answer that is 10 times too big or too small stands out at once.
The steps
- Round each number to its first digit. 48 → 50 and 21 → 20; 387 → 400.
- Calculate with the round numbers. 50 × 20 = 1,000.
- Use the estimate. Say "about 1,000", or compare it with the exact answer (1,008).
Worked examples
Easy Estimate 35 + 39
Show the thinking
35 → 40 and 39 → 40
40 + 40 = 80
So 35 + 39 ≈ 80 (exactly 74).
Answer: 80
Medium Estimate 955 − 587
Show the thinking
955 → 1,000 and 587 → 600
1,000 − 600 = 400
So 955 − 587 ≈ 400 (exactly 368).
Answer: 400
Hard Estimate 48 × 21
Show the thinking
48 → 50 and 21 → 20
50 × 20 = 1,000
So 48 × 21 ≈ 1,000 (exactly 1,008).
Answer: 1,000
When to use it
- Checking a calculator: if 48 × 21 shows 10,080 (480 typed instead of 48), the estimate of 1,000 shows it is 10 times too big.
- Shopping: items at 19.95, 4.1 and 7.8 cost about 20 + 4 + 8 = 32.
When NOT to use it
- When the exact answer matters (a bill, a dose of medicine) — estimate to check, then calculate exactly.
- When rounding moves a number a long way: 150 × 150 becomes 200 × 200 = 40,000, but the real answer is 22,500. Keep two digits instead, or use an exact method.