Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Number
Standard Form
What is Standard Form?
A way of writing any number as A times ten to the power n, where A is at least 1 and less than 10 and n is an integer. It separates the significant digits of a quantity from its scale, which makes very large and very small numbers easy to compare, to multiply and to divide without counting zeros.
This definition is part of the Number chapter in Cambridge O Level Mathematics (Syllabus D).
Standard Form in context
Standard form is \(A\times10^n\) with \(1\le A<10\) and \(n\) an integer. That condition is the whole rule and it is where the marks are: \(18\times10^3\) and \(0.42\times10^6\) are both correct numbers but neither is in standard form, so both must be renormalised to \(1.8\times10^4\) and \(4.2\times10^5\) before the answer is written down.
Common mistakes with Standard Form
- 12. “\(18\times10^{3}\) is in standard form.” Why wrongStandard form requires \(1\le A<10\), and \(18\) fails that. The number is right but the form is not, so the final accuracy mark is lost. Correct\(18\times10^3=1.8\times10^1\times10^3=1.8\times10^4\). Say this“The coefficient must be at least 1 and less than 10, so I renormalise.” CheckWrite \(0.42\times10^{6}\) in standard form. (\(4.2\times10^{5}\).)
Questions students ask about Standard Form
Why does 18 × 10³ count as wrong for standard form?
Standard form requires the coefficient A to satisfy 1 ≤ A < 10, and 18 fails that test even though the number itself is correct. Renormalise it: 18 × 10³ = 1.8 × 10&sup4;.