Physical quantities and measurement

The density equation $\rho = m/V$ is frequently inverted. Dividing volume by mass ($V/m$) gives cm³/g — the reciprocal of density (specific volume), not density — and in a multiple-choice question it is the classic trap. Fix: write $\rho = m/V$ in symbols first, substitute, then check the unit reads kg/m³ or g/cm³ before you choose an option.

In the displacement method you must name what you read from the measuring cylinder as the volume of water. Cambridge does not accept "reading", "height" or "measurement" for that mark. State the physical quantity, not what you observe: record volume $V_1$, lower the solid, record the new volume $V_2$; volume of the solid $= V_2 - V_1$.

Match the final answer to the significant figures of the data. If the data has 2 s.f., give 2 s.f. — rounding to 1 s.f. (0.08 instead of 0.077) loses the mark, and so does quoting 4 decimal places. Significant figures are not decimal places: 0.0045 has 2 s.f.; 0.00450 has 3 s.f.; leading zeros never count.

Every numerical final answer must carry a unit; a correct value with the unit missing still loses the separately-awarded unit mark. Watch the symbol traps too: $t$ is time while $T$ or $\theta$ is temperature, and $E$ is energy while $Q$ is charge. Use the syllabus symbols, and always write the unit — e.g. give a density as 3.0 g/cm³, not 3.0.

Mass is the quantity of matter — a scalar in kg, the same everywhere, measured on a balance. Weight is the gravitational force $W = mg$ — a vector in N, measured with a newton-meter (spring balance), and smaller on the Moon. A spring balance measures a force even when its scale is marked in kg; a beam balance measures mass. Never write a weight in kg.

1 g/cm³ = 1000 kg/m³ (water = 1.0 g/cm³ = 1000 kg/m³). If a question gives grams and cm³ but asks for kg/m³, convert before you start or multiply the g/cm³ answer by 1000 at the end. Mixing units — grams divided by m³ — gives a meaningless g/m³ value that is wrong by a factor of a million.