This module covers what a rounded number really means. You will choose sensible significant figures, recover the interval hidden inside a rounded measurement, find the bounds of sums, differences and products, and decide how accurate a calculated answer can honestly be. The skills appear in area, speed, density and cost questions, and in any question that says “give a reason for your accuracy”.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording of each content point in your exam year. The habits taught here stay the same across versions. Our Mathematics learning guide shows where this module sits among the others.
What should you know before starting?
You should be comfortable rounding to decimal places and significant figures, and with the arithmetic in number sense and exact arithmetic, especially fractions and decimals. You also need to multiply and divide decimals carefully, by hand or by calculator.
A quick orienting example
A water level is read as 12.6 cm to 1 decimal place. What could the true level be?
Any value that rounds to 12.6 works. The rounding unit is 0.1, so the half-unit is 0.05. The smallest value is 12.6 − 0.05 = 12.55, and the largest values approach 12.6 + 0.05 = 12.65.
So the true level satisfies 12.55 ≤ h < 12.65 cm. Every lesson in this module builds on that one idea: a rounded number is an interval, and the rest is about combining intervals sensibly.
In what order should you study the lessons?
- Choose sensible significant figures: start here to be sure you can round and count figures correctly, and avoid rounding too early.
- Recover an interval from a rounded measurement: the half-unit rule that every later lesson uses.
- Bound a sum and a difference: combine two intervals, where the difference needs a crossed pairing.
- Bound a product with positive measurements: areas, costs and speeds, where like is paired with like.
- Distinguish accuracy from displayed decimal places: decide how many figures an answer really deserves.
Finish with the precision bounds practice set. The bounds and rounding explainer draws any interval so you can check your own.
Which traps catch most students here?
- Using the whole unit instead of half, so 7.3 becomes 7.2 to 7.4 rather than 7.25 to 7.35.
- Writing the upper bound as 7.349 instead of 7.35 with a strict inequality.
- Subtracting two lower bounds for the lower bound of a difference.
- Mixing a lower bound with an upper bound in a product.
- Copying the calculator display as if every digit were accurate.
Each lesson shows one of these slips in full and then corrects it.
How should you use the practice set?
Attempt each question on paper before opening the answer, and write your working as you would in an exam. Then mark which questions went wrong and use the routing notes at the end of the practice set to return to the right lesson.
If you want teaching beyond self-study, online one-to-one Mathematics tuition means an experienced teacher looks at your written working and finds which habit is behind the error.