Cambridge IGCSE Mathematics 0580: Estimation and using a calculator – Revision Notes

These notes condense 1.9 Estimation and 1.14 Using a calculator from Topic 1 Number of the Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. The Core (C1.9, C1.14) and Extended (E1.9, E1.14) statements are identical, so every line here is for both tiers; nothing is Extended only. For full explanations and longer worked examples, use the estimation and calculator study guide.

Other pages for this topic: the Number study guide, the Number revision notes, the Number practice questions and the Number (Extended) practice questions. The course sits on the mathematics hub, with a printable checklist for ticking off each statement.

Which papers test this

Paper	Tier	Calculator	1.9 Estimation	1.14 Using a calculator
Paper 1	Core	not allowed	yes	no (excluded by the syllabus)
Paper 2	Extended	not allowed	yes	no (excluded by the syllabus)
Paper 3	Core	scientific calculator required	yes	yes
Paper 4	Extended	scientific calculator required	yes	yes

On Papers 3 and 4 the syllabus sets three accuracy rules:

• Give non-exact answers to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
• Avoid rounding until the final answer. If a later part uses an earlier answer, use the unrounded value.
• Use the π key or 3.142.

1.9.1 Rounding: the rules

Accuracy asked for	Where you count from	Example: 0.006 382	Example: 5097
nearest 10 / 100 / 1000	that column	–	5100 (nearest 100)
decimal places (d.p.)	the decimal point	0.006 (3 d.p.)	–
significant figures (s.f.)	the first non-zero digit	0.0064 (2 s.f.)	5100 (2 s.f.)

Method in steps

1. Mark the last digit you keep.
2. Look ONLY at the next digit.
3. 5 or more -> round the kept digit up; 4 or less -> leave it.
4. Fill gaps before the decimal point with zeros. Keep trailing zeros after it if they are needed to show the accuracy.

Small reminders

7.4951  to 2 d.p.  -> 7.50        (the 0 must stay: 2 d.p. means two digits after the point)
299 600 to 3 s.f.  -> 300 000     (9 rounds up and carries twice)
8.0449  to 1 d.p.  -> 8.0         (look at the 4 only; do not round 8.0449 -> 8.045 -> 8.05 -> 8.1)

The last line is the “double rounding” trap. Round once, from the original number.

Must-know distinctions

• Decimal places vs significant figures. 0.006 382 to 2 d.p. is 0.01; to 2 s.f. it is 0.0064. Read the question twice.
• Leading zeros vs middle zeros. In 0.0064 the zeros before the 6 are not significant. In 5.07 the 0 is significant.
• Placeholder zeros. 5097 to 2 s.f. is 5100, not 51.

1.9.2 Estimating: the method

1. Round EVERY number to 1 s.f. (unless told otherwise).
2. WRITE the rounded calculation down -- this is the method mark.
3. Work it out mentally. Give that as the estimate.

Worked reminder. Estimate (38.6 × 5.12) ÷ 0.207.

38.6 -> 40     5.12 -> 5     0.207 -> 0.2
(40 x 5) / 0.2 = 200 / 0.2 = 1000

Estimate 1000. (The exact value is 954.7…)

Useful mental facts for estimates:

Calculation	Same as
÷ 0.5	× 2
÷ 0.2	× 5
÷ 0.1	× 10
× 0.5	÷ 2

Dividing by a number between 0 and 1 makes the answer bigger. If your estimate went down, check it.

Estimates apply to measurements too: a 2.9 m by 3.8 m wall is about 3 × 4 = 12 m².

1.9.3 Reasonable accuracy in context

Context	Rule
calculator paper, non-exact answer	3 s.f. (angles 1 d.p.) unless told otherwise
exact answer	give it exactly, e.g. 2.5, not 2.50 or “2.5 to 3 s.f.”
money	2 d.p. (nearest cent): a display of 12.6 dollars is written $12.60
“how many are needed”	round up
“how many can be bought / fit / filled”	round down

Worked reminder. 230 eggs are packed in boxes of 6. 230 ÷ 6 = 38.33…

• Boxes needed to hold all the eggs: 39.
• Full boxes that can be filled: 38.

Same division, two different answers. The wording decides.

1.14.1 Using the calculator efficiently

• Do not round inside a calculation. Carry full values with the Ans key or memory.
• Put brackets round a numerator or denominator with more than one term.
• Use the ×10ˣ (EXP) key for standard form.
• Use the π key.
• Do a rough estimate first, so a mis-keyed decimal point stands out.

1.14.2 Entering values

Time: minutes ÷ 60.

Time	In hours
15 min	0.25 h
45 min	0.75 h
24 min	0.4 h
3 h 20 min	3.333… h (enter 3 + 20 ÷ 60, do not type 3.33)

Or use the degrees–minutes–seconds key: 3° 20′ 0″ is 3 h 20 min.

Never type 3 h 20 min as 3.20.

Other entries: convert units first (cm to m, g to kg) so every value is in the same unit; bracket negative numbers before squaring them.

1.14.3 Reading the display

Decimal hours to hours and minutes: decimal part × 60.

1.85 h  -> 0.85 x 60 = 51    -> 1 h 51 min
5.15 h  -> 0.15 x 60 = 9     -> 5 h 9 min      (not 5 h 15 min)

Standard form display. A display such as 2.3E-05 or 2.3×10⁻⁰⁵ means 2.3 × 10⁻⁵ = 0.000 023. Write it in proper notation, never “E-05”.

Money. A display of 6.4 for dollars is written $6.40. A display of 2.666 666 7 for dollars is written $2.67.

“Write down all the figures on your calculator display.” Copy every digit, unrounded. Round in the next step only.

Quick self-test

1. Round 3 849 162 to (a) the nearest thousand, (b) 3 significant figures.
2. Round 0.040 96 to (a) 2 significant figures, (b) 3 decimal places.
3. Round 19.997 to 2 decimal places.
4. (non-calculator) By writing each number correct to 1 significant figure, estimate (9.83 × 21.4) ÷ 0.496.
5. (non-calculator) By writing each number correct to 1 significant figure, estimate √(81.6 + 18.7).
6. (calculator) Write 2 hours 24 minutes in hours as a decimal.
7. (calculator) A calculation gives a time of 5.4 hours. Write this in hours and minutes.
8. 320 people need coach seats. Each coach holds 52 people. How many coaches are needed?
9. (calculator) Work out (5.2 + 3.75) ÷ (1.6 × 0.95). Give your answer correct to 3 significant figures.
10. Notebooks cost $2.70 each. How many can be bought with 40 dollars?
11. (calculator) The display shows 1.2E-05. Write the value as an ordinary number.
12. (calculator) A train travels 84 km in 1 hour 36 minutes. Find its average speed.

Answers

1. (a) 3 849 000 (b) 3 850 000
2. (a) 0.041 (b) 0.041 (here both give the same digits)
3. 20.00 (the 9s carry; keep both zeros)
4. (10 × 20) ÷ 0.5 = 200 ÷ 0.5 = 400 (exact 424.1…)
5. √(80 + 20) = √100 = 10
6. 24 ÷ 60 = 0.4, so 2.4 hours
7. 0.4 × 60 = 24, so 5 hours 24 minutes
8. 320 ÷ 52 = 6.15…, round up: 7 coaches
9. 8.95 ÷ 1.52 = 5.888… = 5.89 (brackets round top and bottom)
10. 40 ÷ 2.70 = 14.8…, round down: 14 notebooks
11. 1.2 × 10⁻⁵ = 0.000 012
12. 1 h 36 min = 1.6 h; 84 ÷ 1.6 = 52.5 km/h (exact, so no rounding needed)

Where marks are usually lost

• Dropping a needed zero: 0.040 to 2 s.f., 7.50 to 2 d.p., 20.00 to 2 d.p.
• Writing 3849 instead of 3 849 000 when rounding to the nearest thousand.
• Counting leading zeros in a small decimal as significant figures.
• Double rounding: rounding a rounded value instead of rounding once from the original.
• Giving an estimate without writing the 1 s.f. values, or rounding only some of the numbers.
• Using normal rounding for whole objects instead of reading “needed” (up) or “can be bought” (down).
• Typing 1 h 36 min as 1.36, or reading 5.15 hours as 5 hours 15 minutes.
• Rounding an intermediate answer and carrying it forward, so the final 3 s.f. answer is out by one in the last digit.
• Leaving money as 6.4 dollars instead of $6.40, or copying “E-05” from the screen as the answer.

Next steps

• Re-read the worked examples in the study guide.
• Apply these skills in the Number practice questions.
• Take the free diagnostic: Core or Extended.

Official syllabus

Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027 (Version 3), Cambridge International. Topic 1 Number, subtopics C1.9 and E1.9 Estimation, and C1.14 and E1.14 Using a calculator.