Cambridge IGCSE Mathematics 0580: Estimation and using a calculator – Study Guide

This study guide teaches two subtopics of Topic 1 Number in the Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027: 1.9 Estimation and 1.14 Using a calculator. The Core statements (C1.9, C1.14) and the Extended statements (E1.9, E1.14) are word-for-word the same, so everything on this page applies to both tiers. There is no Extended-only content in these two subtopics.

The tier affects only which papers you sit. Core candidates take Paper 1 (non-calculator) and Paper 3 (calculator); Extended candidates take Paper 2 (non-calculator) and Paper 4 (calculator). The syllabus says Papers 1 and 2 test everything except Using a calculator (C1.14 and E1.14), so 1.14 is tested only on Papers 3 and 4. Estimation is tested on all four papers.

Use this page with the mathematics course hub and the printable 0580 checklist. For quick recall later, use the estimation and calculator revision notes. The whole of Topic 1 is covered more briefly in the Number study guide and the Number revision notes.

What these subtopics cover

0580 statement	What you must be able to do	Tier
1.9.1	Round values to a specified degree of accuracy, including decimal places and significant figures	Core and Extended
1.9.2	Make estimates for calculations involving numbers, quantities and measurements	Core and Extended
1.9.3	Round answers to a reasonable degree of accuracy in the context of a given problem	Core and Extended
1.14.1	Use a calculator efficiently: do not round values within a calculation, round only the final answer	Core and Extended
1.14.2	Enter values appropriately, e.g. 2 hours 30 minutes as 2.5 hours or 2° 30′ 0″	Core and Extended
1.14.3	Interpret the calculator display appropriately, e.g. 4.8 in money means $4.80	Core and Extended

Bounds (1.10 Limits of accuracy) follow straight on from rounding but are a separate subtopic. They are covered in the Number pages linked above.

1.9.1 Rounding to a specified accuracy

Every rounding question follows the same three steps.

1. Find the last digit you are allowed to keep.
2. Look at the next digit only.
3. If that digit is 5 or more, round the kept digit up. If it is 4 or less, leave it. Then fill any gap before the decimal point with zeros.

Nearest 10, 100 or 1000. The kept digit is in the tens, hundreds or thousands column.

Decimal places (d.p.). Count digits after the decimal point.

Significant figures (s.f.). Count from the first non-zero digit. Zeros at the start of a decimal (0.0…) are never significant. Zeros between non-zero digits are significant (in 4.07 the 0 counts).

Worked example 1

Round 46 285 to (a) the nearest 100, (b) the nearest 1000, (c) 2 significant figures, (d) 4 significant figures.

(a) keep the hundreds digit 2; next digit 8 -> round up      46 300
(b) keep the thousands digit 6; next digit 2 -> leave        46 000
(c) first two s.f. are 4 and 6; next digit 2 -> leave        46 000
(d) first four s.f. are 4, 6, 2, 8; next digit 5 -> round up 46 290

The zeros in 46 000 are placeholders. Writing “46” for (b) changes the size of the number and scores nothing.

Worked example 2

Round 0.070 49 to (a) 1 s.f., (b) 2 s.f., (c) 3 s.f.

first significant figure is the 7 (the 0.0 in front does not count)
(a) 7, next digit 0 -> leave          0.07
(b) 7, 0, next digit 4 -> leave       0.070
(c) 7, 0, 4, next digit 9 -> round up 0.0705

In (b) the final zero must be written. 0.070 shows two significant figures; 0.07 shows only one.

Worked example 3

Round 12.9963 to (a) 2 d.p., (b) 3 s.f.

(a) keep 12.99; next digit 6 -> round the 9 up
    12.99 + 0.01 = 13.00             answer 13.00
(b) keep 12.9; next digit 9 -> round up
    12.9 + 0.1 = 13.0                answer 13.0

When a 9 rounds up it carries into the column to its left. Keep the trailing zeros so the answer still shows the accuracy asked for.

1.9.2 Making estimates

An estimate is a quick, rough answer you can find in your head. In an exam the instruction is usually “by writing each number correct to 1 significant figure, estimate the value of …”. Follow it exactly:

1. Round every number to 1 s.f. and write the rounded calculation down.
2. Work it out with the rounded numbers.
3. Give the estimate. Do not then use a calculator or the original numbers.

Writing the rounded calculation is the method mark. On a non-calculator paper, a bare answer with no rounded values shown may score nothing even if it is right.

Worked example 4 (non-calculator)

Estimate the value of (62.4 × 0.187) ÷ 3.87.

62.4 -> 60      0.187 -> 0.2      3.87 -> 4
(60 x 0.2) / 4 = 12 / 4 = 3

The estimate is 3. (The calculator value is 3.015…, so the estimate is close.)

Worked example 5 (non-calculator)

Estimate the value of (812 + 197) ÷ 0.48.

812 -> 800      197 -> 200      0.48 -> 0.5
(800 + 200) / 0.5 = 1000 / 0.5 = 2000

Dividing by 0.5 is the same as multiplying by 2. Dividing a positive number by a number between 0 and 1 makes the answer bigger, which is a quick check on your working.

Worked example 6 (non-calculator)

Estimate √(0.0385 × 412).

0.0385 -> 0.04      412 -> 400
0.04 x 400 = 16     sqrt(16) = 4

The estimate is 4.

Estimating with measurements

The syllabus includes quantities and measurements, not just bare numbers. A rectangular room measures 4.85 m by 6.12 m. Rounding each length to 1 s.f. gives 5 m × 6 m, so the floor area is about 30 m². The exact area is 29.682 m², so the estimate is a good check.

Estimates are also how you check a calculator answer on Papers 3 and 4. If your estimate is 30 and the display shows 296.82, you have mis-keyed a decimal point.

1.9.3 Rounding answers to a reasonable accuracy

The final answer must make sense for the question.

• Calculator papers: give non-exact answers to 3 significant figures, or angles in degrees to 1 decimal place, unless the question says otherwise. This is the rule written in the syllabus for Papers 3 and 4. Exact answers (such as 2.5 or 120) are given exactly.
• Money: to the nearest cent (2 d.p.), so a display of 7.3 dollars is written $7.30.
• Whole objects: decide whether to round up or down from the context, not from the digit after the point.

Worked example 7

(a) 157 students go on a trip. Each minibus holds 12 students. How many minibuses are needed?

(b) Cinema tickets cost $3.85 each. How many tickets can be bought with 50 dollars?

(a) 157 / 12 = 13.08...   13 buses carry only 156, so round UP    14 minibuses
(b) 50 / 3.85 = 12.98...  13 tickets would cost $50.05, so DOWN  12 tickets

Normal rounding gives 13 in both cases, and 13 is wrong in both. “How many are needed” rounds up; “how many can you afford or fit” rounds down.

1.14.1 Using a calculator efficiently

The syllabus example is to know not to round values within a calculation and only round the final answer. The Paper 3 and 4 instructions say the same: avoid rounding until the final answer, and when a later part uses an earlier answer, use the value before it was rounded.

Efficient habits:

• Use the Ans key (or memory) to carry full values from one step to the next.
• Use brackets round any numerator or denominator with more than one term.
• Use the π key (or 3.142, which the syllabus allows), not 3.14.
• Use the ×10ˣ (or EXP) key for standard form, rather than typing “× 10 ^”.

Worked example 8 (calculator)

A circle has circumference 30 cm. Find (a) its radius, (b) its area.

(a) r = 30 / (2 x pi) = 4.774 648...      radius = 4.77 cm (3 s.f.)
(b) correct: A = pi x Ans^2 = 71.619...    area = 71.6 cm²
    wrong:   A = pi x 4.77^2 = 71.480...   area = 71.5 cm²

Using the rounded radius in (b) gives 71.5, which loses the accuracy mark. Keep 4.774 648… in the calculator.

1.14.2 Entering values appropriately

Time is the most common trap because there are 60 minutes in an hour, not 100.

• Minutes to hours: divide by 60. 1 hour 50 minutes = 1 + 50/60 = 1.8333… hours.
• Or use the degrees–minutes–seconds key (marked ° ′ ″ on most scientific calculators): enter 1° 50′ 0″.

Worked example 9 (calculator)

A car travels 148 km in 1 hour 50 minutes. Find its average speed.

correct:  148 / (1 + 50/60) = 80.727...           80.7 km/h
wrong 1:  148 / 1.50       = 98.666...           98.7 km/h  (typed 1 h 50 min as 1.50)
wrong 2:  148 / 1.83       = 80.874...           80.9 km/h  (rounded the time first)

Wrong 2 shows 1.14.1 and 1.14.2 working together: even the correct conversion, rounded too early, moves the 3 s.f. answer.

Other entries to get right:

• Units: convert to matching units before entering, e.g. 45 cm as 0.45 m if the other lengths are in metres.
• Negative numbers: use brackets when squaring a negative, as the Number revision notes show.
• Fractions: use the fraction key or brackets, so 3/(4 × 5) is not entered as 3 ÷ 4 × 5.

1.14.3 Interpreting the display

The calculator gives a number. You must decide what it means.

Display	Context	Write
15.3	money in dollars	$15.30
0.833 333 3	cost of one item in dollars	$0.83
3.7	time in hours	3 hours 42 minutes (0.7 × 60 = 42)
0.45	time in hours	27 minutes (0.45 × 60 = 27)
4.7 × 10⁻⁰⁴ or 4.7E-04	any	4.7 × 10⁻⁴ = 0.000 47
13.083 333	number of minibuses needed	14

The standard-form display is not an answer in itself. Write it properly as 4.7 × 10⁻⁴, or as an ordinary number if the question asks for one. Never copy “E-04” onto the answer line.

When a question says “write down all the figures on your calculator display”, copy every digit shown, then round in the next part.

Common errors

• Writing 0.07 when 2 s.f. is asked for (0.070), or dropping the zeros in 13.00.
• Counting the zeros in 0.0705 as significant figures.
• Estimating with the original numbers, or not showing the 1 s.f. values.
• Rounding 13.08 minibuses down to 13, or 12.98 tickets up to 13.
• Entering 1 hour 50 minutes as 1.50 or 1.5.
• Reading 3.7 hours as 3 hours 70 minutes.
• Rounding a radius or a time to 3 s.f. and then using it in the next step.
• Copying “4.7E-04” as the answer, or writing $15.3.

Next steps

• Condense this page with the estimation and calculator revision notes.
• Practise with the Number practice questions; Extended candidates can also use the Number (Extended) practice questions.
• Find your gaps across the whole course with 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.