Convert 250\ mm into metres and write the answer in standard form. [2 marks]

SingaporePhysicsSyllabus dot point

How do physicists describe the world using a small set of base quantities, units, and prefixes?

State the SI base quantities and their units, use standard prefixes, and distinguish scalars from vectors

A focused answer to the O-Level Physics outcome on physical quantities. SI base quantities and units, standard prefixes from nano to giga, standard form, and the difference between scalars and vectors.

Generated by Claude Opus 4.87 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
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Examples in context
Try this

What this dot point is asking

SEAB wants you to know the seven SI base quantities and the units physicists use for the ones that appear at O-Level, to use standard prefixes such as kilo, milli, and micro, to write very large or very small numbers in standard form, and to tell the difference between a scalar and a vector. The big idea is that every measurement in physics is a number with a unit, and the unit tells you what kind of quantity it is.

The answer

SI base quantities and units

Physics is built on a small set of base quantities. Each has one agreed SI unit, and every other unit is built from these.

Base quantity	SI unit	Symbol
Length	metre	$\text{m}$
Mass	kilogram	$\text{kg}$
Time	second	$\text{s}$
Electric current	ampere	$\text{A}$
Temperature	kelvin	$\text{K}$
Amount of substance	mole	$\text{mol}$
Luminous intensity	candela	$\text{cd}$

At O-Level the first five matter most. Every other unit, such as the newton or the joule, is a combination of these base units.

Standard prefixes

Prefixes let you write large and small quantities neatly without long strings of zeros.

Prefix	Symbol	Multiplier
giga	$\text{G}$	$10^{9}$
mega	$\text{M}$	$10^{6}$
kilo	$\text{k}$	$10^{3}$
centi	$\text{c}$	$10^{-2}$
milli	$\text{m}$	$10^{-3}$
micro	$\mu$	$10^{-6}$
nano	$\text{n}$	$10^{-9}$

So $3\ \text{km} = 3 \times 10^{3}\ \text{m}$ and $5\ \text{mA} = 5 \times 10^{-3}\ \text{A}$ .

Standard form

Standard form writes a number as a value between $1$ and $10$ multiplied by a power of ten. It keeps very large and very small numbers readable and makes the prefix obvious:

0.0025\ \text{m} = 2.5 \times 10^{-3}\ \text{m} = 2.5\ \text{mm}

Scalars and vectors

A scalar has size only. A vector has both size and direction.

Scalars: distance, speed, mass, time, energy, temperature.
Vectors: displacement, velocity, acceleration, force, weight, momentum.

Two scalars add by ordinary arithmetic. Two vectors only add simply if they point the same way; if they point in opposite directions you subtract, and the direction of the result matters.

Worked example

A student walks $30\ \text{m}$ east, then $40\ \text{m}$ west. Find the total distance travelled and the final displacement from the start.

Step 1: Add the distances as scalars

Distance ignores direction, so it is just the total path length: $30 + 40 = 70\ \text{m}$ .

Step 2: Treat displacement as a vector

Take east as positive. The displacement is $+30\ \text{m}$ then $-40\ \text{m}$ , giving $30 - 40 = -10\ \text{m}$ .

Step 3: State the displacement with direction

The result is $10\ \text{m}$ in the negative direction, that is $10\ \text{m}$ west of the start.

So the student travels a distance of $70\ \text{m}$ but ends only $10\ \text{m}$ west of where they began. Distance and displacement are different because one ignores direction and the other does not.

Examples in context

Example 1. Reading a data sheet. A resistor is labelled $4.7\ \text{k}\Omega$ . The prefix kilo means $\times 10^{3}$ , so its resistance is $4700\ \Omega$ . Recognising prefixes lets you convert any labelled value into base units before substituting into a formula.

Example 2. Adding velocities. A swimmer moves at $1.5\ \text{m s}^{-1}$ across a river while the current carries them downstream. Because velocity is a vector, the two motions combine by direction, not by simple addition, which is why the swimmer ends up downstream of the point opposite their start.

Try this

Q1. State the SI base unit, with symbol, for length, mass, and time. [2 marks]

Cue. Length: metre, $\text{m}$ . Mass: kilogram, $\text{kg}$ . Time: second, $\text{s}$ .

Q2. Convert $250\ \text{mm}$ into metres and write the answer in standard form. [2 marks]

Cue. $250\ \text{mm} = 250 \times 10^{-3}\ \text{m} = 0.25\ \text{m} = 2.5 \times 10^{-1}\ \text{m}$ .

Q3. Explain why velocity is a vector but speed is a scalar. [2 marks]

Cue. Speed states only how fast (magnitude); velocity states how fast and in which direction, so it has both magnitude and direction.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original4 marks(a) State the SI base unit of mass, of length, and of time. (b) Write

0.000\,045\ \text{m}

in standard form and then in micrometres (

\mu\text{m}

Show worked answer →

(a) Mass is measured in the kilogram ( $\text{kg}$ ), length in the metre ( $\text{m}$ ), and time in the second ( $\text{s}$ ).

(b) Standard form: $0.000\,045\ \text{m} = 4.5 \times 10^{-5}\ \text{m}$ .

Since $1\ \mu\text{m} = 10^{-6}\ \text{m}$ , divide by $10^{-6}$ : $4.5 \times 10^{-5}\ \text{m} = 45\ \mu\text{m}$ .

Markers reward the three correct base units with symbols, the value written as a number between $1$ and $10$ times a power of ten, and the correct conversion to micrometres.

Original3 marksClassify each of the following as a scalar or a vector: distance, displacement, speed, velocity, mass, force. Explain what extra information a vector carries that a scalar does not.