Describe the SI base quantities and their units, choose suitable instruments to measure length, volume, mass and time, and read those instruments to the correct precision

What this dot point is asking

SEAB wants you to know the main physical quantities and the units we measure them in, to pick the right instrument for a given measurement, and to read that instrument carefully and to the correct precision. The key idea is that every measurement in science is a number together with a unit, and the unit is just as important as the number.

The answer

Physical quantities and SI units

A physical quantity is something we can measure. Each one has an agreed SI (International System) unit so that scientists everywhere mean the same thing. The base quantities you need are:

• Length, measured in metres ($\text{m}$).
• Mass, measured in kilograms ($\text{kg}$).
• Time, measured in seconds ($\text{s}$).
• Temperature, measured in kelvin ($\text{K}$) or degrees Celsius ($^\circ\text{C}$).

Other quantities are built from these. For example, volume is length cubed, measured in cubic metres ($\text{m}^3$) or, more usefully in the lab, cubic centimetres ($\text{cm}^3$).

Common prefixes

Prefixes let us write very large or very small values neatly:

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

To convert centimetres to metres you divide by $100$; to convert metres to centimetres you multiply by $100$.

Choosing the right instrument

The instrument must match the size of what you are measuring:

• Length: a metre rule for everyday lengths, vernier calipers for small objects such as a marble, a micrometer screw gauge for very thin objects such as a wire.
• Volume of a liquid: a measuring cylinder. For the volume of a small irregular solid, lower it into water and measure how much the water level rises (the displacement method).
• Mass: an electronic balance.
• Time: a stopwatch or digital timer.

Reading a scale correctly

To read any scale accurately, look at it straight on, with your eye level with the marking. Looking from an angle gives a parallax error. With a measuring cylinder, read the bottom of the curved liquid surface, called the meniscus.

Examples in context

Example 1. Measuring the thickness of a coin. A single coin is too thin to measure reliably with a ruler. Stack $20$ identical coins, measure the total height (say $30\ \text{mm}$), then divide: one coin is $30 \div 20 = 1.5\ \text{mm}$. Measuring many and dividing reduces the effect of the reading error.

Example 2. Timing a swinging pendulum. A pendulum swings too fast to time one swing accurately. Time $10$ complete swings (say $16\ \text{s}$) and divide by $10$ to get one swing: $1.6\ \text{s}$. The same trick of measuring many and dividing makes the result more reliable.

Try this

• Cue. Convert $250\ \text{cm}$ into metres. Divide by $100$ to get $2.5\ \text{m}$.
• Cue. A measuring cylinder reads $42\ \text{cm}^3$, then $58\ \text{cm}^3$ after a marble is added. State the marble's volume: $58 - 42 = 16\ \text{cm}^3$.
• Cue. Explain why you should time $20$ swings of a pendulum rather than one. Dividing the total time by $20$ reduces the effect of your reaction-time error, giving a more reliable value for one swing.