Units and Maths Skills » Units, Prefixes and Significant Figures

Speaking the language of chemistry

Chemistry has its own vocabulary. Words like reactant, product, mixture and compound have exact meanings. In an exam, a loose answer such as "the chemical goes away" loses marks, but "the reactant is used up" earns them. Use the correct term every time, and use the definitions you have met in this course. This applies to every topic, including the required practicals.

Chemists also name substances in a standard way. The international system is called IUPAC nomenclature. It means a chemist in any country uses the same name for the same substance. For example, we write sodium chloride, not "salt", and ethanol, not "alcohol" or "spirits". Note the spelling of sulfur: sulfuric acid and copper sulfate use an f. Only use a common name when the question uses it first.

Key terms:

• Quantity: something you can measure, such as mass, volume, temperature, time or energy.
• SI units: the international standard units that scientists agree to use for quantities.
• IUPAC name: the standard international name for a chemical, so everyone means the same substance.
• Prefix: a short word placed before a unit that multiplies it by a power of ten.

Scientific quantities and how we measure them

A scientific quantity is something we can measure with a number and a unit. It is important because numbers let us compare results, spot patterns and check predictions. "A lot of acid" is useless, but "25.0 cm³ of acid" can be repeated by anyone.

Each quantity is found with a suitable piece of equipment:

Some quantities are worked out from others. For example, a rate of reaction comes from an amount of product divided by the time taken. Energy is measured in joules (J) or kilojoules (kJ).

SI units and prefixes

Scientists use SI units. The ones you meet most in chemistry are the kilogram (kg), gram (g) and milligram (mg) for mass; the kilometre (km), metre (m) and millimetre (mm) for length; and the joule (J) and kilojoule (kJ) for energy. Use them unless the question clearly needs something else.

Look at the names. Kilo, milli and so on are prefixes. A prefix tells you how many times bigger or smaller a unit is than the basic unit. You need to know these:

So 1 kg is 1000 g, 1 km is 1000 m, and 1 kJ is 1000 J. In the other direction, 1 mm is one thousandth of a metre, so 1 m is 1000 mm. A nanometre (nm) is one thousand millionth of a metre. Nanoparticles are between 1 and 100 nanometres across.

These powers of ten link to orders of magnitude: a kilometre is three orders of magnitude bigger than a metre.

Changing one unit into another

To interconvert units, remember one rule:

• Going from a bigger unit to a smaller unit: there will be more of them, so multiply.
• Going from a smaller unit to a bigger unit: there will be fewer of them, so divide.

Volume: cm³ and dm³

Volumes in chemistry are usually measured in cm³ (cubic centimetres). Many calculations need dm³ (cubic decimetres). A dm³ is a cube measuring 10 cm × 10 cm × 10 cm, so:

1 dm³ = 1000 cm³

Converting with powers of ten works too. Centi is 10^-2, so 5 cm = 5 × 10^-2 m = 0.05 m. Micro is 10^-6, so 20 µm = 20 × 10^-6 m = 2.0 × 10^-5 m. Nano is 10^-9, so 3.2 nm = 3.2 × 10^-9 m.

Using an appropriate number of significant figures

The rule for calculations is simple: give your answer to the same number of significant figures as the least precise number you used. An answer cannot be more precise than the measurements it came from.

Count significant figures from the first digit that is not zero. Zeros at the start do not count, but zeros after other digits in a measurement do. So 0.00406 has 3 significant figures and 25.0 also has 3.

Exam-style question

A student measures 35.0 cm³ of acid and 0.0250 dm³ of alkali.

(a) Write 35.0 cm³ in dm³. (b) Write 0.0250 dm³ in cm³. (c) The student works out 4.2 ÷ 0.0250 and the calculator shows 168. Give the answer to a suitable number of significant figures.