Significant Figures
Rounding to a sensible accuracy
In this note
- 1.9Give answers to the accuracy asked - otherwise 3 significant figures (angles to 1 decimal place).
- 1.9Keep enough figures in the working: don't round too early.
- 1.9Round to fit the context: money, people, containers.
Before you start: rounding and estimation.
Formula bank
The exam's accuracy rules
| Situation | Give your answer | Example |
|---|---|---|
| The question says how | exactly that | "to 2 s.f." → 7.9 |
| Nothing is said | exact, or 3 s.f. | 126.676… → 127 |
| Angles | 1 d.p. | 57.783…° → 57.8° |
| Money | 2 d.p. | $41.7 → $41.70 |
| A count of things | a whole number, up or down | 2.86 tins → 3 |
General methodHow to give any calculator answer
- Do the whole calculation, keeping full values (Ans key or memory).
- Write the full display.
- Round once, to the accuracy asked (or the default).
- Context: money to the cent; counts up or down as the story needs.
Example Calculate \(\dfrac{5.67+2.09^{2}}{1.38\times0.917}\) to 2 s.f.
Brackets, full value, then 2 s.f.
- \(10.0381\div1.265\,46=7.932\,37\ldots\)
Answer 7.9
Try it yourself
Show answer
Answer 12.25
Show answer
Answer 0.1429
Show answer
Answer 127
Don't round too early
Rounding in the middle and then reusing the rounded value makes the error grow. A square of area 20 cm² has side \(\sqrt{20}=4.472\ldots\); the cube with that edge has volume 89.4 cm³. Cube the rounded 4.47 and you get 89.3, cube 4.5 and you get 91.1: both wrong.
Try it yourself
Hint
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Answer 25.07
A sensible accuracy
An answer can't be more accurate than its data. A radius measured as 6.35 cm (3 s.f.) gives an area of 126.676… cm², but only 127 cm² is trustworthy. For things you count, round to whole numbers in the direction the story needs.
Try it yourself
Show answer
Answer 3
Ways they test it
Type 1 Calculate to a given accuracy
"Calculate … Give your answer correct to 2 significant figures." (2 marks)
Spot it an accuracy in the question.
- Full value (B1).
- Rounded as asked (B1).
Type 2 No accuracy given
"A circle has radius 6.35 cm. Calculate its area."
Spot it "calculate" with no accuracy.
- Full value.
- 3 s.f. (angles 1 d.p.).
For example r = 6.35
- \(\pi\times6.35^{2}=126.676\,8\ldots\)
Answer 127 cm²
Type 3 Multi-step: keep the full value
"A square has area 20 cm². Find the volume of the cube with the same edge." (3 marks)
Spot it a value found then reused.
- Keep it in the calculator.
- Round only the end.
For example side \(\sqrt{20}\)
- \((\sqrt{20})^{3}=89.44\ldots\)
Answer 89.4 cm³
Type 4 Money and containers
"Paint is sold in 2.5-litre tins at $13.90. Find the cost." (4 marks)
Spot it tins, buses, money.
- Litres needed.
- Tins: round UP.
- Cost to the cent.
For example 7.14 litres needed
- \(7.14\div2.5=2.86\ldots\) → 3 tins
- \(3\times13.90\)
Answer $41.70
Mistakes to avoid
- ✗ 7.93 when 2 s.f. was asked✓ 7.9Do what the question says.
- ✗ Rounding a side to 4.47 and then cubing✓ cube the full valueErrors grow.
- ✗ 57.78° for an angle✓ 57.8°Angles to 1 d.p.
- ✗ $41.7✓ $41.70Money to the cent.
Summary
- Follow the instruction; otherwise 3 s.f., angles 1 d.p., money 2 d.p.
- Write the full value, then round once, at the end.
- Counts: round up or down to fit the story.
If you see …
- a value you will use againkeep it in the calculator.
- "tins", "buses", "boxes"decide: up or down?
Practice
Practice: easy, medium, hard
Easy
Show answer
Answer 57.8
Show answer
Answer 127
Show answer
Answer $41.70
Medium
Guide me
What is it asking? the value to 2 s.f.
What do we know? a cube
Plan full value 385.83…, then 2 s.f.
Show working
- 385.83…
- 3, 8 | 5 → up
Answer 390
Guide me
What is it asking? the volume
What do we know? \(\pi r^{2}h\)
Plan full value, then 3 s.f.
Show working
- \(\pi\times6.25\times7.1=139.408\ldots\)
Answer 139
Guide me
What is it asking? the value
What do we know? brackets top and bottom
Plan full value, then 2 s.f.
Show working
- \(7.932\ldots\)
Answer 7.9
Hard
Guide me
What is it asking? the volume
What do we know? side \(\sqrt{20}\)
Plan cube the FULL value
Show working
- \((\sqrt{20})^{3}=89.442\ldots\)
Answer 89.4
| Part | Answer / working | Marks | Guidance |
|---|---|---|---|
| \(\sqrt{20}\) | M1 | ||
| \((\sqrt{20})^{3}\) | M1 | ||
| 89.4 | A1 | ||
| Total: 3 marks | |||
Guide me
What is it asking? the cost
What do we know? area, litres, tins, money
Plan round tins UP
Show working
- \(67.86\) m²
- \(7.14\) litres
- 2.86 → 3 tins
- \(3\times13.90\)
Answer $41.70
| Part | Answer / working | Marks | Guidance |
|---|---|---|---|
| 67.86 | M1 | ||
| 7.14… | M1 | ||
| 3 tins | M1 | ||
| 41.70 | A1 | ||
| Total: 4 marks | |||
Guide me
What is it asking? the circumference
What do we know? area 50
Plan \(r=\sqrt{50/\pi}\), keep it, then \(2\pi r\)
Show working
- \(r=3.989\ldots\)
- \(2\pi r=25.066\ldots\)
Answer 25.07
| Part | Answer / working | Marks | Guidance |
|---|---|---|---|
| \(r=\sqrt{50/\pi}\) | M1 | ||
| 25.07 | A1 | not 25.13 from r = 4 | |
| Total: 2 marks | |||
Can I do this?
- I know the default accuracy rules (3 s.f., angles 1 d.p., money 2 d.p.).
- I keep full values and round only at the end.
- I can choose a sensible accuracy and round counts to fit.
Anything unticked: revise that section first. All ticked: take the quiz.
Quiz
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