Measuring like a scientist

SI units · Standard form · Significant figures

Physics · 1A · 16 September 2026

Today: 4 steps

Recall

What did we measure?

SI units

One language for everyone

Standard form

Very big, very small

Significant figures

How many digits are true?

Then: exercises, in silence.

The case of the impossible stopwatch

A runner, 100 m.
A witness times him with a phone.
The screen shows 11.3748 s.
Holmes: “The witness is claiming too much.”

STOPWATCH

11.3748

seconds

Vote with your hand: why?

The app is broken.
A finger cannot press STOP so precisely.
Nobody runs 100 m in 11 s.

We close the case at the end of the lesson.

LAST LESSON

Recall 1 · The scale

How many digits after the decimal point?
How many digits in total?

12.37\ \mathrm{g}

LAST LESSON

Recall 2 · The stopwatch

How many digits after the decimal point?

08.46

This stopwatch: 08.46 · The phone in the case: 11.3748

WHERE DOES THE UNCERTAINTY COME FROM?

Recall 3 · Pressing STOP

You see the runner cross the line.
Your brain reacts.
Your finger moves.
How long does all this take?

Typical visual reaction time ≈ 0.2–0.25 s. Source: Jain et al., Int. J. Appl. Basic Med. Res. 5(2), 2015.

SI units

SYSTÈME INTERNATIONAL

Base quantities

Quantity	Unit	Symbol
length	metre	m
mass	kilogram	kg
time	second	s
electric current	ampere	A
temperature	kelvin	K
amount of substance	mole	mol
luminous intensity	candela	cd

7 base units.
Every other unit is built from these.

Source: BIPM, The International System of Units (SI Brochure), 9th ed., 2019.

BUILT FROM BASE UNITS

Derived quantities

area \mathrm{m^2}

length × length

volume \mathrm{m^3}

length × length × length

speed \mathrm{m/s}

length ÷ time

density \mathrm{kg/m^3}

mass ÷ volume

POWERS OF TEN

Prefixes

1 km = 10³ m = 1000 m
1 mg = 10⁻³ g
1 μs = 10⁻⁶ s
1 nm = 10⁻⁹ m

G	10⁹
M	10⁶
k	10³
—	10⁰
c	10⁻²
m	10⁻³
μ	10⁻⁶
n	10⁻⁹

STEP DOWN: THE NUMBER GETS BIGGER

Worked examples · Simple conversions

2.5\ \mathrm{km}\rightarrow \mathrm{m}

1 km = 1000 m

2.5\times 1000

2500 m

350\ \mathrm{g}\rightarrow \mathrm{kg}

1 kg = 1000 g

350\div 1000

0.350 kg

CONVERT ONE UNIT AT A TIME

Worked example · 72 km/h in m/s

72\ \mathrm{km/h}=\dfrac{72\times1000\ \mathrm{m}}{3600\ \mathrm{s}}

1 km = 1000 m, 1 h = 3600 s

=\dfrac{72\,000\ \mathrm{m}}{3600\ \mathrm{s}}

multiply first

=20\ \mathrm{m/s}

then divide

Standard form

DEFINITION

Standard form

RULE

A number in standard form is a\times 10^{n}, with 1\le a\lt 10 and n an integer.

✓ correct

3.84\times 10^{5}\ \mathrm{m}

✗ not standard form

38.4\times 10^{4}\ \mathrm{m}

WORKED EXAMPLES

Two steps

384\,000\ \mathrm{km}

→ move the point 5 places left

3.84\times 10^{5}\ \mathrm{km}

0.000\,45\ \mathrm{m}

→ move the point 4 places right

4.5\times 10^{-4}\ \mathrm{m}

Big number → positive power. Small number → negative power.

Significant figures

4 RULES

Which digits count?

1	Non-zero digits count.	12.37 g → 4
2	Zeros between digits count.	105 s → 3
3	Leading zeros never count.	0.0045 m → 2
4	Final zeros after the point count.	3.00 kg → 3

COMMON MISTAKE

The calculator trap

Data · significant figures

mass = 6\times 10^{24}\ \mathrm{kg}\ \rightarrow 1

volume = 1.09\times 10^{21}\ \mathrm{m^3}\ \rightarrow 3

Calculator: 5521.4 kg/m³

Answer: 6×10³ kg/m³

× or ÷ → count the significant figures of each number in the data.

Your answer gets the smallest count.

BACK TO HOLMES

Case closed: the answer is B

Reaction time ≈ 0.2 s — the uncertainty is in the tenths of a second.
The last three digits mean nothing. Honest result: 11.4 s.

World record, 100 m

9.58 s

Source: World Athletics, men's 100 m world record, Usain Bolt, Berlin 2009.

20 MINUTES · IN SILENCE · ALONE

Now you work

Worksheet: start from Section A.
Write every step, not only the result.
Stuck? Raise your hand and wait.
Not finished? It is your homework.