Physical quantities, units and measurement

Study quantities, SI units, scale, instruments, scalars, vectors and graphical vector addition.

SEC G3 Physics 2027

Learning goals

Represent a physical quantity with a numerical magnitude and unit
Recall the six prescribed SI base quantities and their units
Use the prescribed SI prefixes from nano to tera
Compare orders of magnitude from a typical atom to the Earth
Select and justify measuring instruments by range and precision
Distinguish scalar and vector quantities and give examples
Add two vectors graphically to determine a resultant

Measurement and graphical vectors

Measurement questions reward correct units, suitable instruments and a clear method. Follow this route before using the skills in mechanics and practical work.

New to the topic? Begin with base quantities and SI units, then follow the ordered lesson list below. If you are already confident with units, start at measurement of length.

Lessons

Base quantities and SI units
Recall the six base quantities listed for 6091 and distinguish base from derived units.
CoreOpen lesson
Prefixes and conversions
Use powers of ten and convert squared or cubed units correctly.
CoreOpen lesson
Measurement of length
Choose a tape, rule, digital caliper or digital micrometer by range and precision.
CoreOpen lesson
Measurement of time
Use a digital stopwatch and measure periods reliably.
CoreOpen lesson
Measurement quality and errors
Separate accuracy from precision and improve systematic or random errors.
CoreOpen lesson
Scalars and vectors
Distinguish magnitude-only quantities from quantities that also require direction.
CoreOpen lesson
Vector addition
Add two vectors by a scale drawing and state the resultant magnitude and direction.
CoreOpen lesson

Calipers and micrometers

G3 Physics and O-Level practical work uses digital calipers and digital micrometers. Each lesson also shows the analogue scale in case your school or a question uses one.

Digital and vernier calipers
Zero and read a digital caliper, and read an analogue vernier scale if you meet one.
CoreOpen lesson
Digital and screw-gauge micrometers
Close a micrometer with the ratchet, check its zero and correct the reading.
CoreOpen lesson

Beyond the syllabus

Practice: reading a vernier caliper
Read main and vernier scales on caliper diagrams with no zero error.
OptionalOpen lesson
Practice: finding vernier zero error
Find positive and negative zero errors from closed-jaw readings.
OptionalOpen lesson
Practice: corrected vernier readings
Subtract the zero error from each observed reading.
OptionalOpen lesson

Revision

High-value checks

Write every measurement as a number and a unit.
Use mutually consistent units in an equation and give the requested output unit.
Choose an instrument whose range includes the value and whose precision is suitable.
Record all digits justified by the instrument display or scale.
Correct a zero error using: corrected reading = observed reading − zero error.
Repeat measurements to reveal scatter and calculate a mean when appropriate.

Six base quantities to recall

Base quantity	SI unit	Symbol
mass	kilogram	kg
length	metre	m
time	second	s
electric current	ampere	A
temperature	kelvin	K
amount of substance	mole	mol

The complete SI system has a seventh base quantity, luminous intensity, measured in candela. For this course, recall the six quantities above.

Check your understanding

Worked example: A digital caliper shows 12.36 mm for the diameter of a ball. Its zero reading is + 0.04 mm. The corrected diameter is

12.36-0.04 = 12.32 mm.

The correction is subtraction because corrected reading = observed reading − zero error. Keeping the unit in the final answer is part of reporting a physical quantity properly.

Practise this: Two forces act at right angles: 3.0 N east and 4.0 N north. Draw them head-to-tail using a stated scale, then measure the resultant’s magnitude and direction. Your drawing should give about 5.0 N, 53° north of east.

Practice

Complete structured measurement questions to practise method, calculation and data-recording marks.
Use the measurement quiz to check definitions, instruments and conversions.

Use the Measurement check for quantities, units, prefixes, instruments and vector addition. If you need to combine directed quantities, study vector addition by graphical methods first.

Continue learning

Continue to O-Level practical skills for planning and evaluation, or begin kinematics to use units, timing and vectors in motion.

Useful applications within later topics include:

Practise

Practise: Physical quantities, units and measurement

A text-first Measurement assessment with labelled response controls and explicit quantities, units, powers of ten and vector directions.

About 10 minutes

Practise

Questions are selected when you start. Use the feedback to decide what to practise next; this does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

This check needs JavaScript to record answers. The reviewed questions are listed below for study.

A wire diameter is 0.00045 m. Which equivalent value is correct?

0.45 without a unit
45 mm
0.00045 mm
0.45 mm

Which pair correctly matches a base quantity to its SI base unit?

temperature — kelvin (K)
mass — gram (g)
time — minute (min)
length — kilometre (km)

A bacterium is about 10⁻⁶ m and a grain of sand about 10⁻³ m. How many orders of magnitude separate them?

3
−9
2
1000

What micrometer reading is shown?

The sleeve scale shows 6.5 mm and the thimble datum aligns with division 28. The micrometer has no zero error. Each thimble division represents 0.01 mm.

6.28 mm
34.5 mm
6.78 mm
6.50 mm

Which quantity is a vector?

mass
velocity
speed
energy

Two perpendicular vectors are drawn as 3.0 cm east and 4.0 cm north using 1.0 cm for 1.0 N. What should be measured for the resultant?

The arrow from the first tail to the final head; it is 5.0 cm long and points about 53° north of east.
A 7.0 cm arrow east, found by adding lengths only.
A 1.0 cm arrow south, found by subtracting lengths.
A 5.0 cm line with no arrow or direction.

Practise

Practise after feedback: Physical quantities, units and measurement

A text-first Measurement assessment with labelled response controls and explicit quantities, units, powers of ten and vector directions.

About 10 minutes

Practise

Questions are selected when you start. Use the feedback to decide what to practise next; this does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

This check needs JavaScript to record answers. The reviewed questions are listed below for study.

A student writes the period of a pendulum as 2.4. What is missing?

Nothing; a number alone is a complete physical quantity.
A unit, such as 2.4 s.
A direction, because every measurement is a vector.
A prefix, because every SI unit needs one.

Which is an SI base unit?

joule
coulomb
ampere
newton

A time interval is 3.6 ms. What is it in seconds?

0.0036 without a unit
3.6 s
3600 s
0.0036 s

An atom is about 10⁻¹⁰ m across and the Earth about 10⁷ m across. Roughly how many orders of magnitude separate them?

A vernier caliper reads +0.06 cm when fully closed. How is a later reading corrected?

Add 0.06 cm
Ignore the zero error
Subtract 0.60 cm
Subtract 0.06 cm

A car travels 5 km south then 5 km north. Which statement is correct?

Distance is 10 km and displacement is 5 km north
Distance is 10 km and displacement is zero
Both distance and displacement are 10 km
Distance is zero and displacement is zero

Where does the resultant arrow begin and end in a two-vector head-to-tail construction?

It joins the two arrowheads.
It begins at the second head and points back to the first tail.
It joins the midpoints of the two arrows.
It begins at the first vector's tail and ends at the second vector's head.

Vernier caliper trainer

Interactive vernier readings with a static instrument-reading fallback.

About 8 minutes

Practise choosing the vernier reading from labelled main-scale and vernier-scale values.

Open the vernier caliper trainer

Micrometer trainer

Interactive micrometer readings with a static instrument-reading fallback.

About 8 minutes

Practise combining the sleeve and thimble readings and checking for zero error.

Open the micrometer trainer

Check what I know

Check what I know: Physical quantities, units and measurement

A text-first Measurement assessment with labelled response controls and explicit quantities, units, powers of ten and vector directions.

About 8 minutes

Check what I know

Answer 7 short questions. This starting check helps choose what to work on; it does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

This check needs JavaScript to record answers. The reviewed questions are listed below for study.

A student writes the period of a pendulum as 2.4. What is missing?

Nothing; a number alone is a complete physical quantity.
A unit, such as 2.4 s.
A direction, because every measurement is a vector.
A prefix, because every SI unit needs one.

Which is the prescribed SI base unit for electric current?

coulomb (C)
volt (V)
watt (W)
ampere (A)

Convert 3.2 ms to seconds.

3.2 × 10⁻⁶ s
0.32 s
3.2 × 10⁻³ s
3.2 × 10³ s

An atom is about 10⁻¹⁰ m across and the Earth about 10⁷ m across. Roughly how many orders of magnitude separate them?

Which instrument is most suitable for the internal diameter of a small pipe?

A measuring tape wrapped around the pipe.
A stopwatch, because it gives a digital reading.
A digital caliper using its internal jaws.
A digital micrometer placed across the outside.

Which statement distinguishes velocity from speed?

Velocity includes direction as well as magnitude and unit; speed does not.
Speed includes direction but velocity does not.
Both are vectors because both use m/s.
Both are scalars because direction is optional.

How should two vectors be placed for a head-to-tail graphical addition?

Place both tails together and add only their drawn lengths.
Reverse the second vector before drawing it.
Ignore the scale because only the arrow directions matter.
Draw the second vector with its tail at the head of the first, preserving scale and direction.

Check my progress

Check my progress: Physical quantities, units and measurement

A text-first Measurement assessment with labelled response controls and explicit quantities, units, powers of ten and vector directions.

About 10 minutes

Check my progress

Answer 7 questions. If accepted, this result can contribute to your course progress.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Check again

Check again: Physical quantities, units and measurement

A text-first Measurement assessment with labelled response controls and explicit quantities, units, powers of ten and vector directions.

About 10 minutes

Check again

Answer 7 questions. If accepted, this result can contribute to your course progress.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Review

Review: Physical quantities, units and measurement

A text-first Measurement assessment with labelled response controls and explicit quantities, units, powers of ten and vector directions.

About 10 minutes

Review

Answer 7 questions. A scheduled review can contribute to your course progress only when it is due and the result is accepted.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

How this activity affects progress

Course and syllabus information

Course: SEC G3 Physics
Edition: SEC G3 Physics 2027

Physical quantities, units and measurement

Measurement and graphical vectors

Lessons

Base quantities and SI units

Prefixes and conversions

Measurement of length

Measurement of time

Measurement quality and errors

Scalars and vectors

Vector addition

Calipers and micrometers

Digital and vernier calipers

Digital and screw-gauge micrometers

Beyond the syllabus

Practice: reading a vernier caliper

Practice: finding vernier zero error

Practice: corrected vernier readings

Revision

Check your understanding

Practice

Continue learning

Practise: Physical quantities, units and measurement

Practice complete

Practise after feedback: Physical quantities, units and measurement

Practice complete

Vernier caliper trainer

Micrometer trainer

Check what I know: Physical quantities, units and measurement

Starting check complete

Check my progress: Physical quantities, units and measurement

Progress check complete

Check again: Physical quantities, units and measurement

Progress check complete

Review: Physical quantities, units and measurement

Review complete