SI units — seven base units and all derived units: Foundations

The first split: quantity vs unit vs number

Why the topic needs this. When the parent says "seven base units", it means seven agreed standard chunks. When it says "seven base quantities", it means the seven kinds of thing those chunks measure. Confuse the two and the whole table looks like nonsense. Look at the figure: the coloured chunk is the unit, the count of chunks is the number, the ruler itself is the quantity.

The symbol every recipe uses: powers

Before force or energy, you must read expressions like $s^{- 2}$ and $m^{2}$ .

Why the topic needs this. The base unit of force is written $kg\cdotm\cdots^{- 2}$ . That $s^{- 2}$ is not decoration — it literally means "divided by second, divided by second again". The parent's whole table is powers of the seven sticks; if you can't read a negative exponent, you can't read a single derived unit.

The ratio: what "per" really means

Why the topic needs this. Almost every derived unit is a "per": speed is m per s, pressure is force per area, voltage is energy per charge. The word "per" is the engine that stacks the powers. Look at the figure — the same journey read as "how far in one second" gives the ratio; that ratio is the derived unit.

The bracket notation: $[\cdot]$ means "the units of"

Why the topic needs this. The parent writes $[F] = [m] [a]$ . This is the master move: units multiply the same way the physics equation multiplies. If $F = ma$ , then $[F] = [m] \cdot [a]$ . The brackets let you throw away the numbers and track only the sticks. This is the seed of Dimensional Analysis.

The idea of a "basis": why exactly seven

Why the topic needs this. The parent claims seven is the minimum complete set. "Complete" = every quantity is reachable; "minimum" = you can't drop one. That is exactly the definition of a basis. Look at the figure: three independent arrows reach every point in the room; a fourth arrow lying in the same room would be redundant — mixable from the first three.

Powers-of-ten and prefixes (the kilo in kilogram)

Why the topic needs this. The parent's one genuine oddity is that the base unit of mass is the kilogram, not the gram. A prefix is baked into the base unit's name. You need to see a prefix as just a number multiplier to accept that $kg$ (not $g$ ) is the official stick.

How it all feeds the topic

Each foundation on the left must be solid before the "derive any unit" box — and that box is the parent topic. The bracket notation also opens the door to Dimensional Analysis, and the base quantities length/time reappear everywhere in Kinematics — velocity and acceleration, Newton's Laws of Motion and Work, Energy and Power.

Worked micro-example: build a speed unit from zero

Equipment checklist

Test yourself — each should be an instant "yes".

I can say what the number, unit, and quantity are in "

5 kg

number

= 5

, unit

=

kilogram, quantity

=

mass.

I can read

s^{- 2}

in plain words.

"divided by second, squared" i.e.

1/ s^{2}

I know what

x^{0}

equals.

1

I can turn "metres per second" into a power expression.

m\cdots^{- 1}

I know what the bracket

[F]

means.

"the units (dimension) of

F

I can state the rule linking

F = ma

to units.

[F] = [m] [a]

— units multiply the same way the equation does.

I can say why there are exactly seven base units.

they are independent (none built from the others) and complete (all else mixable) — a basis.

I know why the kilogram, not the gram, is base.

officially the kilogram is the SI base unit of mass; the prefix is baked in.

I know a prefix changes the size but not the kind of quantity.

yes — kilometre and metre both measure length.

Recall One-line summary

Learn to read powers, ratios, and the bracket $[\cdot]$ , plus the basis idea "seven independent sticks", and the parent topic becomes pure bookkeeping.