№12 · NUMBER · FOUNDATION + HIGHER
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gcsemathsai
EST. MMXXIV · LONDON · MMXXVI SPEC.
№ 12 · XII
NUMBER · FOUNDATION + HIGHER
A4 · 210×297mm
NumberFoundation + Higher

Estimation.
Rounding for sanity checks.

An estimate is a quick, sensible approximation — rounded to 1 significant figure. Used to check whether a calculator answer is reasonable. If your estimate and your actual differ wildly, you've slipped up.
I · Key definitions
Estimate
An approximate calculation, using rounded values.
289 ≈ 300
1 s.f.
Round to one significant figure.
47 → 50 · 0.273 → 0.3
Significant
Counting from the first non-zero digit.
0.00473 — first s.f. is 4
Actual
The exact answer (calculator).
estimate vs actual comparison
≈ symbol
Means 'approximately equal to'.
287 ≈ 300
Check
An estimate is a sanity check on your answer.
estimate ≈ actual → ✓
II · The estimation method
Step-by-step
1. Round each number to 1 s.f.
2. Calculate with the rounded values
3. State the estimate · compare to actual
Estimate (287 × 19) / 0.48 → (300 × 20) / 0.5 = 6000/0.5 = 12,000
III · Rounding to 1 s.f. · examples
287
↓
300
19
↓
20
0.48
↓
0.5
3972
↓
4000
0.00634
↓
0.006
52.7
↓
50
Keep only the first non-zero digit. Everything else becomes 0 (but keep place value).
IV · Worked examples
Estimate a calculation
3 marks
Estimate the value of   (287 × 19) / 0.48.
i.Round each to 1 s.f.: 287 → 300 · 19 → 20 · 0.48 → 0.5
ii.Calculate: (300 × 20) / 0.5 = 6000 / 0.5
iii.= 6000 × 2 = 12,000
Estimate ≈ 12,000
Estimate with squares
3 marks
Estimate √(39² + 28²).
i.Round: 39 → 40 · 28 → 30
ii.40² + 30² = 1600 + 900 = 2500
iii.√2500 = 50
Estimate ≈ 50
V · Common mistakes & examiner tips
Common mistakes
Rounding to 2 s.f. when asked for 1. 287 to 1 s.f. = 300, not 290.
Not rounding 0.48 — people leave it thinking it's 'already small'.
Giving the actual answer instead of an estimate. The point is to be quick & sensible.
Dividing by 0.5 = × 2 forgotten. Quick tricks save time.
Estimating after calculating. Defeats the purpose — do it first!
Examiner tips
Round first, calculate second.
Dividing by a small decimal makes it bigger. 1 ÷ 0.5 = 2.
Use estimates to check if your calculator answer is about right.
Show all workings — method marks for the rounding steps.
Common sense check: does your estimate make sense for the real-world context?
© GCSEMATHSAI · MMXXVI SPEC · PRINT & STICK
gcsemathsai.co.uk · /sheets/12
SQUARE · 900 × auto · Social-ready
Σ
gcsemathsai
EST. MMXXIV · LONDON · MMXXVI SPEC.
№ 12 · XII
NUMBER · FOUNDATION + HIGHER
Square · 1:1
NumberFoundation + Higher

Estimation.
Rounding for sanity checks.

An estimate is a quick, sensible approximation — rounded to 1 significant figure. Used to check whether a calculator answer is reasonable. If your estimate and your actual differ wildly, you've slipped up.
I · Key definitions
Estimate
An approximate calculation, using rounded values.
289 ≈ 300
1 s.f.
Round to one significant figure.
47 → 50 · 0.273 → 0.3
Significant
Counting from the first non-zero digit.
0.00473 — first s.f. is 4
Actual
The exact answer (calculator).
estimate vs actual comparison
≈ symbol
Means 'approximately equal to'.
287 ≈ 300
Check
An estimate is a sanity check on your answer.
estimate ≈ actual → ✓
II · The estimation method
Step-by-step
1. Round each number to 1 s.f.
2. Calculate with the rounded values
3. State the estimate · compare to actual
Estimate (287 × 19) / 0.48 → (300 × 20) / 0.5 = 6000/0.5 = 12,000
III · Rounding to 1 s.f. · examples
287
↓
300
19
↓
20
0.48
↓
0.5
3972
↓
4000
0.00634
↓
0.006
52.7
↓
50
Keep only the first non-zero digit. Everything else becomes 0 (but keep place value).
IV · Worked examples
Estimate a calculation
3 marks
Estimate the value of   (287 × 19) / 0.48.
i.Round each to 1 s.f.: 287 → 300 · 19 → 20 · 0.48 → 0.5
ii.Calculate: (300 × 20) / 0.5 = 6000 / 0.5
iii.= 6000 × 2 = 12,000
Estimate ≈ 12,000
Estimate with squares
3 marks
Estimate √(39² + 28²).
i.Round: 39 → 40 · 28 → 30
ii.40² + 30² = 1600 + 900 = 2500
iii.√2500 = 50
Estimate ≈ 50
V · Common mistakes & examiner tips
Common mistakes
Rounding to 2 s.f. when asked for 1. 287 to 1 s.f. = 300, not 290.
Not rounding 0.48 — people leave it thinking it's 'already small'.
Giving the actual answer instead of an estimate. The point is to be quick & sensible.
Dividing by 0.5 = × 2 forgotten. Quick tricks save time.
Estimating after calculating. Defeats the purpose — do it first!
Examiner tips
Round first, calculate second.
Dividing by a small decimal makes it bigger. 1 ÷ 0.5 = 2.
Use estimates to check if your calculator answer is about right.
Show all workings — method marks for the rounding steps.
Common sense check: does your estimate make sense for the real-world context?
© GCSEMATHSAI · MMXXVI SPEC · PRINT & STICK
gcsemathsai.co.uk · /sheets/12