Number and Numeration
Number and numeration
A candidate must move confidently between fractions, decimals, percentages and standard form, and must apply place value when ordering or rounding. Know the meanings of factor, multiple, prime, square, cube and reciprocal; be able to find HCF and LCM by listing or prime factorisation. Directed-number rules, the order of operations (brackets, indices, multiplication and division, then addition and subtraction) and the index laws are examined frequently.
Typical traps include treating -3^2 as 9 when it is -9, while (-3)^2 is 9; rounding too early in a multi-step calculation; writing 34 x 10^5 instead of 3.4 x 10^6 in standard form; and confusing HCF with LCM in word problems. When a question asks for a value to a given number of significant figures, keep more digits until the final line. For recurring decimals, use the algebraic subtraction method rather than guessing.
Worked rule: evaluate 5 - 2^3 / 4 + (-3). Indices first: 2^3 = 8. Then division: 8 / 4 = 2. The expression becomes 5 - 2 - 3 = 0. Notice that the negative sign belongs to the 3, and subtraction is performed left to right.
For standard form, write A x 10^n with 1 <= A < 10. Thus 0.00042 = 4.2 x 10^-4. Always check the direction of the decimal shift.