Units and significant figures in SPM Chemistry answers

Two of the easiest marks to lose in SPM Chemistry have nothing to do with how hard the chemistry is. They are the unit you forgot to write and the final answer given to the wrong number of figures. Both are recall and habit, not understanding, which means both are completely within your control. This post is about turning them into automatic wins.

A number without a unit is often marked wrong

In a calculation question, the final line usually carries a mark for the value and, separately, the correct unit. Write 0.10 where the mark scheme wants 0.10 mol and you can lose that unit mark even though your arithmetic is perfect. The safest habit is to write the unit at the same moment you write the number, every single time, all the way through the working, not just on the last line.

Writing units through the working also protects you in a second way: it tells you when something has gone wrong. If your quantities multiply out to give g cm⁻³ but the question asked for a concentration in mol dm⁻³, the mismatch is a warning that you have used the wrong formula or the wrong data.

The units you actually meet in SPM Chemistry

You only need a small, fixed set. Learn them as a table and the guessing stops:

• Mass: g (sometimes kg)
• Amount of substance: mol
• Molar mass: g mol⁻¹
• Relative atomic / molecular / formula mass: no unit at all (it is a ratio)
• Concentration: mol dm⁻³ or g dm⁻³
• Volume of solution: cm³ or dm³
• Volume of gas: dm³ or cm³, measured at stated conditions
• Heat change: J or kJ
• Heat of reaction: kJ mol⁻¹
• Temperature: °C for readings, K where the question asks
• Rate of reaction: cm³ s⁻¹, g s⁻¹ or mol dm⁻³ s⁻¹
• Density: g cm⁻³

Notice that relative atomic mass, relative molecular mass and relative formula mass have no unit. They are ratios against one-twelfth of a carbon-12 atom, so writing “16 g” for the relative atomic mass of oxygen is wrong. Molar mass, which does carry g mol⁻¹, is the one that looks similar but is a different quantity.

The trap: cm³ versus dm³

The single most common unit slip is mixing cm³ and dm³. Concentration in SPM is mol dm⁻³, but volumes of solution are usually measured in cm³. Since 1 dm³ = 1000 cm³, you must divide a volume in cm³ by 1000 before using it in a concentration formula.

Worked example. What is the concentration of a solution containing 0.25 mol of sodium hydroxide in 500 cm³?

• Convert the volume: 500 cm³ = 500 / 1000 = 0.500 dm³
• Concentration = mol / volume = 0.25 / 0.500 = 0.50 mol dm⁻³

Skip the conversion and you would divide by 500, giving 0.0005 mol dm⁻³, a hundredfold error from one unit slip. Our calculation questions guide and the step-by-step methods on our chemistry calculations hub drill exactly this conversion, and the mole calculator lets you check your own working while you practise.

How many significant figures should the final answer have?

Give the final answer to a sensible number of significant figures, matching the precision of the data you were given, in SPM this is almost always three significant figures. If a question hands you masses like 4.50 g and 12.0 g (three figures each), a final answer of 0.0375 mol is right; writing 0.04 mol throws away precision, and writing 0.037500000 mol claims precision the data does not support.

A few working rules:

• Count from the first non-zero digit. In 0.0375, the significant figures are 3, 7 and 5, the leading zeros do not count.
• Match, do not exceed, the data. Three-figure data deserves a three-figure answer.
• Significant figures are not the same as decimal places. 0.0375 has three significant figures but four decimal places; 12.0 has three significant figures but one decimal place.
• Do not round in the middle of a multi-step calculation. Keep the full value in your calculator and round only the final answer, or the small rounding error grows as it passes through each step.

That last point matters enough that we treat it separately, see our companion post on rounding and rounding errors for how premature rounding can push an otherwise correct answer outside the accepted range.

A quick self-check before you write the final line

When you reach the last line of a calculation, pause for three seconds and ask:

1. Have I written a unit next to this number?
2. Is it the unit the question asked for, mol dm⁻³, not mol, if it wanted a concentration?
3. Is the answer to about three significant figures?
4. Does the size look reasonable, a school-lab concentration is usually a small number like 0.1 to 2 mol dm⁻³, not 5000?

Those four checks take almost no time and routinely save two or three marks across a full Paper 2. Over a whole paper, careful units and figures can be the difference between grade boundaries, which is why our experienced SPM Chemistry teachers, spend real lesson time marking students’ scripts the way an examiner would.

Small habits, real marks

None of this needs new chemistry. It needs the discipline to attach a unit to every number and to report a final answer honestly, to the precision your data allows. If you would like someone to catch these leaks in your own written answers, our online one-to-one lessons run in English from RM50 an hour, with a paid one-hour trial. Fix the units and the figures, and the marks your knowledge has already earned actually reach your script.