Number and Numeration
What you must understand
Number and numeration rewards precision rather than speed. A candidate needs fluent work with place value, standard form (scientific notation), rounding and significant figures, fractions, decimals and percentages, ratio and proportion, directed numbers, factors, multiples, primes, squares and cubes, and the laws of indices and surds. You should be able to move between equivalent forms: fractions to decimals to percentages, improper fractions to mixed numbers, and ordinary numbers to standard form.
Traps that appear in questions
- Rounding too early. Carry full accuracy through a calculation and round only the final answer.
- Significant figures versus decimal places. Do not confuse them; leading zeros are never significant.
- Percentage change direction. A 20% increase followed by a 20% decrease does not return to the original value.
- Ratio sharing. Convert the ratio to a total number of parts before dividing the amount.
- Order of operations. Brackets, indices, multiplication and division, then addition and subtraction.
- Standard form. The coefficient must lie between 1 and 10; watch negative powers for small numbers.
Worked example
Share $240 in the ratio 3:5. Total parts = 3 + 5 = 8. One part = 240 ÷ 8 = 30. Shares are 3 × 30 = $90 and 5 × 30 = $150. Check: 90 + 150 = 240.
Rule of thumb
When a question says estimate or approximate, round each number to one significant figure first, then calculate; when it says exact, keep every digit and simplify at the end.