This module covers the skills for writing numbers compactly and exactly. They are index laws with negative and fractional powers, standard form for very large and very small numbers, and comparing quantities by size. They also include simplifying roots and estimating to check answers. These skills support science calculations, algebra, bounds and later geometry.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording of each content point in your exam year. The habits here stay the same across versions. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You need times tables, square numbers up to 15², and comfort with fractions and decimals. The number sense and exact arithmetic module covers those foundations. You do not need algebra yet, though the index laws will return there.
An orienting example
Find the value of (9 × 10−4)1/2, giving your answer in standard form.
The power 1/2 means a square root, and it applies to both parts of the product.
Take the square root of 9, which is 3. For the power of ten, (10−4)1/2 = 10−4 × 1/2 = 10−2. So the answer is 3 × 10−2.
Check: 9 × 10−4 = 0.0009, and √0.0009 = 0.03 = 3 × 10−2. One example used index laws, a root and standard form together, which is how exam questions often combine them.
In what order should you study the lessons?
- Apply index laws with negative powers: everything else in the module relies on it.
- Convert a small measurement to standard form: the negative power of ten in a real context.
- Compare quantities with different powers of ten: uses standard form to decide which is bigger and by how much.
- Simplify a root using square factors: exact roots, using the idea that √(a × b) = √a × √b.
- Estimate the size of a standard-form answer: pulls everything together as a check.
Then try the mixed practice set, which has twelve original questions with full explanations.
What are the common traps?
- Reading a negative power as a negative number. 2−3 is 1/8, not −8.
- Counting zeros instead of places when writing a small number in standard form.
- Comparing only the decimal parts and ignoring the power of ten.
- Pulling a square factor out of a root without square-rooting it, such as √72 = 36√2.
- Trusting the calculator display without a rough size check.
How do you use the practice set well?
Attempt each question on paper before opening the answer.
Compare your working with the explanation, line by line. When you miss one, the “If you got these wrong” table at the end of the practice set points you to the relevant lesson. The non-calculator working trainer gives extra practice at exact working.
After this module, precision, bounds and measurement builds on the estimating and size-checking habits.
If index laws and standard form still trip you up, or you skip the check step, a teacher in online one-to-one Mathematics tuition can watch you work and correct the habit as it happens.