State the SI base quantities and units, use common prefixes, and choose suitable instruments to measure length and time

What this dot point is asking

SEAB wants you to state the SI base quantities and their units, to use common prefixes such as kilo, centi and milli, to convert between units, and to choose a sensible instrument for measuring length and time. The big idea is that every measurement in physics is a number together with a unit, and that the unit and the precision both matter.

The answer

Physical quantities and SI units

A physical quantity is anything we can measure. It is always written as a number multiplied by a unit, for example $2.5\ \text{m}$ or $30\ \text{s}$. Physics uses the SI system (the international system of units) so that everyone agrees on the same units.

There are a small number of base quantities. The three you meet most often at this level are:

• Length, with base unit the metre ($\text{m}$).
• Mass, with base unit the kilogram ($\text{kg}$).
• Time, with base unit the second ($\text{s}$).

Other quantities are built from these. For example, speed is length divided by time, so its unit is metres per second ($\text{m s}^{-1}$).

Prefixes

A prefix is a short word put in front of a unit to make it bigger or smaller. They save us writing long strings of zeros. The ones you need are:

• kilo ($\text{k}$) means $\times 1000$, so $1\ \text{km} = 1000\ \text{m}$.
• centi ($\text{c}$) means $\div 100$, so $1\ \text{cm} = 0.01\ \text{m}$.
• milli ($\text{m}$) means $\div 1000$, so $1\ \text{mm} = 0.001\ \text{m}$.

To convert, multiply or divide by the value of the prefix. Going from a big unit to a small unit gives a bigger number, and going from a small unit to a big unit gives a smaller number.

Choosing an instrument for length

Pick the instrument that matches the size and the precision you need:

• A metre rule measures up to a metre, to the nearest millimetre.
• A measuring tape measures longer distances such as the length of a room.
• A pair of calipers measures small lengths such as the diameter of a rod more precisely than a rule.

Always read a scale with your eye directly in front of the mark to avoid a parallax error.

Choosing an instrument for time

A stopwatch or digital timer measures time. For a short, repeating event such as a pendulum swing, time many swings and divide. This is because your reaction time when starting and stopping is a fixed error, and dividing a large total by the number of swings makes that error a much smaller fraction of each result.

Examples in context

Example 1. A running track. A coach measures a sprint distance as $0.10\ \text{km}$. To compare it with a stopwatch time in seconds, the distance is converted to $100\ \text{m}$. Keeping length in metres and time in seconds means the speed comes out directly in $\text{m s}^{-1}$, the SI unit.

Example 2. The thickness of paper. A single sheet of paper is far too thin to measure with a rule. A student measures the thickness of a stack of 500 sheets as $50\ \text{mm}$ and divides: each sheet is $50 \div 500 = 0.1\ \text{mm}$. Measuring many and dividing is the same trick used for timing a pendulum.

Try this

• Cue. Convert $3.4\ \text{m}$ into millimetres. [1 mark] Multiply by 1000 because there are $1000\ \text{mm}$ in a metre: $3.4 \times 1000 = 3400\ \text{mm}$.

• Cue. A student times 10 swings of a pendulum and gets $14\ \text{s}$. Find the time for one swing and say why 10 swings were timed. [2 marks] One swing $= 14 \div 10 = 1.4\ \text{s}$; timing 10 swings reduces the percentage error from reaction time.

• Cue. Name a suitable instrument to measure the diameter of a thin wire and explain your choice. [2 marks] A pair of calipers (or a micrometer), because a metre rule is not precise enough for such a small length.