GCSE science units, prefixes and significant figures: a parent guide

Units, symbols and nomenclature, explained

The curriculum asks students to develop their scientific vocabulary and to understand that scientific quantities, such as mass, force, energy or current, are defined carefully and determined by measuring something specific. For example, speed is found from distance and time, and density from mass and volume. Words that mean one thing in everyday speech have a precise meaning in science. Weight is a force, not an amount of matter, and a “theory” is a tested explanation. Students are taught to use the exact term, because examiners award marks for it.

The standard system of units used by scientists is called SI. The base units students meet most often are the metre (m) for length, the kilogram (kg) for mass, the second (s) for time, the ampere (A) for current, the kelvin (K) for temperature and the mole (mol) for amount of substance. Other units are built from these, such as the newton (N) for force, the joule (J) for energy and the watt (W) for power. Some familiar units, such as the litre, the minute and the kilowatt-hour, are not SI but are still used where convenient, which is what the phrase “unless inappropriate” allows for. In chemistry, students also use the systematic naming rules agreed by the international body for chemistry, called IUPAC. These give names such as sodium chloride, calcium carbonate, copper(II) sulfate (spelled with an f), ethanol and propane.

Prefixes let us write quantities that are very large or very small without long strings of zeros. The curriculum lists tera (10¹², a million million), giga (10⁹), mega (10⁶), kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶, written µ) and nano (10⁻⁹). A nanometre is a millionth of a millimetre. Students are also expected to talk about orders of magnitude, which means roughly how many powers of ten bigger or smaller one quantity is than another. A hair is about 0.1 mm wide, or 100 micrometres, so a virus about 100 nanometres across is around a thousand times smaller, three orders of magnitude.

Interconverting units means changing a quantity from one unit to another without changing its size, for example 3.7 mA into amperes (0.0037 A), or 2.5 GJ into joules (2.5 × 10⁹ J, or 2,500,000,000 J). The trick is to know what the prefix means as a number: milli means a thousandth, so milliamperes are divided by 1,000 to get amperes. Many mistakes in physics calculations come from forgetting to do this before using an equation. A good habit is to convert everything into base SI units first, do the calculation, and then check that the units of the answer make sense.

Finally, students must use an appropriate number of significant figures. The first non-zero digit is the first significant figure, so 0.0037 has 2 significant figures, and 0.00450 has 3. In a calculation, the answer should not be given to more significant figures than the least precise number used. A calculator might show 8.14 with many more digits, but if the data were given to 2 significant figures, the answer should be as well. Rounding is done at the end, not in the middle of a calculation.

Words your child will hear

SI unit

A unit from the international system, such as the metre, kilogram, second or ampere.

Prefix

A word part put in front of a unit to scale it, such as kilo (×1,000) or milli (÷1,000).

Standard form

A way to write numbers as a value between 1 and 10 times a power of ten, such as 3.7 × 10⁻³.

Order of magnitude

A rough size measured in powers of ten. 1,000 is three orders of magnitude bigger than 1.

Significant figures

The digits in a number that carry meaning, starting from the first non-zero digit.

Quantity

A property that can be measured, such as mass or time, as opposed to the unit used to measure it.

IUPAC name

The internationally agreed systematic name of a chemical, such as ethanol or sodium chloride.

What the National Curriculum says

The programme of study for Key Stage 4 says:

• Students should develop understanding and first-hand experience of developing their use of scientific vocabulary and nomenclature
• Students should develop understanding and first-hand experience of recognising the importance of scientific quantities and understanding how they are determined
• Students should develop understanding and first-hand experience of using SI units and IUPAC chemical nomenclature unless inappropriate
• Students should develop understanding and first-hand experience of using prefixes and powers of ten for orders of magnitude (e.g. tera, giga, mega, kilo, centi, milli, micro and nano)
• Students should develop understanding and first-hand experience of interconverting units
• Students should develop understanding and first-hand experience of using an appropriate number of significant figures in calculations

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Common mistakes and how to help

How to help at home

• Convert as you cook. Change a recipe quantity between units: 750 g into kilograms, or 0.25 litres into millilitres. Ask whether the number should get bigger or smaller before working it out. It trains the “which unit is larger” check.
• Find prefixes in everyday life. Look for kilo, mega, giga and tera on broadband speeds, phone storage, food packaging and the electricity bill, which uses kilowatt-hours. Ask your teenager what each prefix means as a number.
• Scale up and down. Estimate the sizes of familiar things in powers of ten: a hair at about 0.1 mm, a grain of sand, a classroom, the distance to the next town. Then express each in metres, in standard form if possible. A nanometre is a millionth of a millimetre.
• Read chemical names on labels. Look at ingredient lists and cleaning products for names like sodium chloride, calcium carbonate and ethanol. Ask what each name tells you about the elements in it, such as the ending “-ide” or “-ate”.

Related topics

Everything in Key Stage 4 science