Estimate Questions
Estimation Skills
"Estimate" questions test your ability to:
- Round numbers sensibly
- Perform calculations without a calculator
- Check whether answers are reasonable
The Rules of Estimation
- Round each number to 1 significant figure (usually)
- Perform the calculation with the rounded values
- Show your rounded values clearly
- Don't round your final estimate (keep it exact from rounded inputs)
Standard Estimation Process
Question: Estimate the value of $\frac{48.7 \times 6.12}{0.236}$
Step 1 — Round to 1 s.f.:
- $48.7 \approx 50$
- $6.12 \approx 6$
- $0.236 \approx 0.2$
Step 2 — Calculate: $\frac{50 \times 6}{0.2} = \frac{300}{0.2} = 1500$
Step 3 — Present clearly: $\frac{48.7 \times 6.12}{0.236} \approx \frac{50 \times 6}{0.2} = 1500$
When to Round Differently
Sometimes 1 s.f. doesn't give nice numbers. Use judgement:
- $\sqrt{48}$ → round to $\sqrt{49} = 7$ (not $\sqrt{50}$)
- $\pi \approx 3$ for estimation
- Numbers like 34 might round to 35 or 30 depending on the calculation
Estimation for Checking
Use estimation to verify your calculator answers:
If calculating: $23.4 \times 18.7 = ?$
Estimate: $20 \times 20 = 400$
Calculator says: $437.58$ ✓ (reasonable)
If calculator said: $43.758$ — you'd know something was wrong!
Common Estimation Contexts
Area and Perimeter:
- Round measurements first
- Estimate whether your answer is sensible for the real-world object
Percentage Problems:
- 19% ≈ 20% (or $\frac{1}{5}$)
- 52% ≈ 50% (or $\frac{1}{2}$)
- 9% ≈ 10% (or $\frac{1}{10}$)
Large Numbers:
- Population of 67,400,000 ≈ 70,000,000 or $7 \times 10^7$
- £385,420 ≈ £400,000
"Explain Why This Is an Estimate"
A common follow-up question. Good answers include:
- "The values have been rounded, so the answer is approximate"
- "The exact values were not used in the calculation"
- "Rounding introduces inaccuracy, so this is not the precise answer"
Warning: Don't Over-Round Your Answer
Once you've estimated with rounded values, give the exact result:
❌ $\frac{50 \times 6}{0.2} \approx 1000$ (don't round again!) ✅ $\frac{50 \times 6}{0.2} = 1500$