The SI System: Base Units

Locked in a vault at Sèvres, outside Paris, under three nested glass bell jars, sits a golf-ball-sized cylinder of platinum-iridium known as Le Grand K. From 1889 to 2019 it did not represent the kilogram — it was the kilogram: to know any mass on Earth was to compare it, through an unbroken chain of copies, to that one object. Then metrologists noticed something alarming: against its own official sister copies, Le Grand K had drifted by roughly $50\ \mathrm{\mu g}$ over a century — the mass of a fingerprint — and the comparisons could not even say whether the copies had grown heavier or the original lighter. Either way, the world's definition of mass was changing, and every balance on the planet was chained to it. In 2019 the chain was cut. Today all seven SI base units are defined by fixing the exact numerical values of seven constants of nature. No artefact, no vault, no drift: a laboratory in Delhi, Geneva or on Mars can realise the kilogram from the Planck constant and get precisely the same unit. For you, these seven units are the operating system of every formula you will ever use — and exams harvest marks from unit fluency relentlessly: prefix slips ( $1\ \mathrm{km^2} \neq 1000\ \mathrm{m^2}$ ), grams smuggled into SI formulas, mis-written symbols. This article gives the seven definitions the modern way, the powers-of-ten grammar of prefixes, and the conversion machinery JEE-Main turns into a question almost every year.

Key takeaways

The SI has exactly seven base units — metre, kilogram, second, ampere, kelvin, mole, candela — and every other unit is built from them.
Since 2019 each is defined by fixing a constant of nature exactly: the second by the caesium frequency, the metre by $c$ , the kilogram by the Planck constant $h$ — no physical artefacts remain.
The definitions cascade: second first, then the metre (via $c$ ), then the kilogram (via $h$ ).
Prefixes are pure powers of ten — and they obey the exponent: $1\ \mathrm{km^2} = (10^3\ \mathrm{m})^2 = 10^6\ \mathrm{m^2}$ .
A measurement is the invariant product $n \times u$ : shrink the unit and the number grows in compensation — the see-saw behind every conversion.
Key idea: a unit is an agreed standard of comparison; the SI pins seven of them to exact constants of nature, and everything else in measurement is powers-of-ten bookkeeping on top of those seven.

The core insight

Seven base units, each now defined by fixing the exact value of a constant of nature, form the complete foundation of measurement — every other unit, every prefix and every conversion is a product of powers of these seven.

Where this lives today

The kilogram is now realised — turned from definition into hardware — by the Kibble balance, which weighs a mass against a magnetic force measured purely electrically, in quantum units that involve $h$ . NIST's and BIPM's balances reach a few parts in $10^8$ ; any equipped lab can now realise the kilogram independently — no more flights to Paris with a padlocked case. Meanwhile the second's definition lives on borrowed time: optical lattice clocks near $10^{-18}$ outperform caesium a hundredfold — so sensitive that raising one a few centimetres in Earth's gravity measurably shifts its rate. A redefinition is pencilled in. And the seven-unit machine runs in your pocket: GPS satellites carry atomic clocks realising the SI second, broadcasting time signals your phone converts — via the fixed $c$ , equation (1) working overtime — into your position within metres. Every 5G tower and stock-exchange timestamp is a downstream customer of the caesium tick.

The physical picture

Strip any measurement to its skeleton and it is a comparison: this desk is 1.4 times an agreed stick called the metre (the framing of Physical Quantities & Measurement). The game of metrology is choosing the sticks and ticks well. Choose physical objects, and standards can be scratched, stolen or — as Le Grand K proved — drift. Choose recipes anchored to constants of nature, and anyone, anywhere, forever can rebuild them exactly. That is the modern SI: seven base quantities, seven units, seven fixed constants.

Figure

The seven SI base units and the constants that define them

Notice what the cards claim. The constants are not measured any more — they are fixed by decree, and the units inherit their sizes from those decrees. Before 2019 we measured $h$ in terms of a kilogram defined by a cylinder; now we define the kilogram in terms of an $h$ declared exact. The uncertainty didn't vanish — it moved into the realisation, the craft of building a balance or clock good enough to use the definition. And the seven are not independent: the second stands alone, the metre leans on the second, the kilogram on both (through $h$ , whose unit $\mathrm{J\,s} = \mathrm{kg\,m^2\,s^{-1}}$ contains them). Definitions cascade — which is why every definition question starts with the second.

Seven units, seven constants

The full set, in cascade order:

quantity	unit	fixed constant	the definition in one line
time	second (s)	$\Delta\nu_{\mathrm{Cs}} = 9\,192\,631\,770\ \mathrm{Hz}$	1 s = 9 192 631 770 cycles of the caesium-133 hyperfine radiation
length	metre (m)	$c = 299\,792\,458\ \mathrm{m/s}$	1 m = distance light travels in vacuum in $1/299\,792\,458$ s
mass	kilogram (kg)	$h = 6.626\,070\,15 \times 10^{-34}\ \mathrm{J\,s}$	fixing $h$ ( $\mathrm{kg\,m^2\,s^{-1}}$ ) pins the kg once m, s are known
electric current	ampere (A)	$e = 1.602\,176\,634 \times 10^{-19}\ \mathrm{C}$	1 A = 1 coulomb per second, the coulomb counted in charges $e$
temperature	kelvin (K)	$k_B = 1.380\,649 \times 10^{-23}\ \mathrm{J/K}$	1 K = the step that changes thermal energy $k_BT$ by a fixed number of joules
amount of substance	mole (mol)	$N_A = 6.022\,140\,76 \times 10^{23}\ \mathrm{mol^{-1}}$	1 mol = exactly $N_A$ entities — a pure count
luminous intensity	candela (cd)	$K_{cd} = 683\ \mathrm{lm/W}$	pins light as the eye sees it to the watt

The second deserves its strange number explained. Caesium-133 atoms absorb and emit microwaves at one extremely sharp, universal frequency when flipping between two hyperfine states; a caesium clock locks onto that transition and counts cycles — at $9\,192\,631\,770$ , one second has passed. The ugly number was chosen in 1967 to match the astronomical second already in use, so no clock jumped when the definition changed. The metre then rides on the second. Light in vacuum covers distance at the universal rate $c$ , so distance is delivered by a stopwatch:

d = c\,t \qquad (1)

where: $d$ — distance travelled by light in vacuum (m); $c = 299\,792\,458\ \mathrm{m/s}$ , exact by definition; $t$ — the light-travel time (s). Read it as a definition, not a formula: since $c$ is fixed, measuring a length has become measuring a time — the quantity we measure best in all of physics. A 30 cm ruler is "the distance light crosses in about a nanosecond" ( $0.30/2.998\times10^8 = 1.0 \times 10^{-9}\ \mathrm{s}$ ).

Derivation AFrom a caesium tick to the metre stick

We want to show how two definitions — the caesium second and the fixed speed of light — combine to produce a metre that needs no artefact, and to check the construction is exactly self-consistent. The strategy is to build the units in the order the SI does: realise one second by counting cycles, let light run for that second, then carve the distance into the defined fraction. Watch where measurement ends and decree begins: the caesium frequency and $c$ are exact by convention; only our apparatus is imperfect.

Step 1. Realise the second: lock a microwave source to the caesium-133 hyperfine transition and count cycles. By definition, $9\,192\,631\,770$ cycles $= 1\ \mathrm{s}$ exactly. Why caesium: the frequency is a property of every caesium atom in the universe — identical in Delhi and Geneva, immune to drift; two good clocks disagree by under a second in 100 million years.

Step 2. Let light fly: in vacuum light travels at $c$ , so in exactly one second it covers $d = c \times 1\ \mathrm{s} = 299\,792\,458$ metres — by decree, since $c$ is fixed, not measured.

Step 3. Carve out the unit: define $1\ \mathrm{m}$ as the distance covered in $t = \frac{1}{299\,792\,458}\ \mathrm{s}$ . Then $d = c\,t = 299\,792\,458 \times \frac{1}{299\,792\,458} = 1$ — one metre, exactly, no rounding anywhere. Why this direction: we could have fixed the metre and measured c forever (as before 1983). Fixing c means better experiments make our rulers better instead of changing a constant — the constant anchors, the hardware varies.

Step 4. Sanity-check the scale: light crossing a $10\ \mathrm{m}$ classroom takes $10/(2.998\times10^8) = 3.34\times10^{-8}\ \mathrm{s}$ — 33 nanoseconds. Length metrology is time metrology plus a beam of light. Verified: $299\,792\,458 \times (1/299\,792\,458) = 1$ exactly; $0.30\ \mathrm{m}/(2.998\times10^8\ \mathrm{m/s}) = 1.00\times10^{-9}\ \mathrm{s}$ ; $10/(2.998\times10^8) = 3.34\times10^{-8}\ \mathrm{s}$ recomputed.

The kilogram completes the cascade. The Planck constant carries the unit $\mathrm{J\,s} = \mathrm{kg\,m^2\,s^{-1}}$ ; with the metre and second defined and $h$ declared exact, only one size of kilogram makes the units of $h$ come out right — and the Kibble balance (see Where this lives today) realises it. For exams the machinery is not needed; "since 2019 the kilogram is defined by fixing the Planck constant" is the expected sentence on CBSE, ICSE and IB papers alike.

Prefixes: the powers-of-ten grammar

Physics spans the femtometre nucleus to the terametre solar system — 27 powers of ten. Rather than invent new units, the SI attaches prefixes, each a pure power of ten, to the same base units:

x = a \times 10^{n}\, u \qquad (2)

where: $x$ — the physical quantity; $a$ — the numerical part; $u$ — the unit; $10^n$ — the prefix's power. A prefix is nothing but a folded-in power of ten: $5\ \mathrm{km} = 5 \times 10^3\ \mathrm{m}$ , $700\ \mathrm{nm} = 7\times10^{-7}\ \mathrm{m}$ — no new physics, only bookkeeping. The ladder every board expects cold: pico ( $10^{-12}$ ), nano ( $10^{-9}$ ), micro ( $10^{-6}$ ), milli ( $10^{-3}$ ), centi ( $10^{-2}$ ), kilo ( $10^{3}$ ), mega ( $10^{6}$ ), giga ( $10^{9}$ ), tera ( $10^{12}$ ).

Figure

The prefix ladder, and the trap when units are squared

The right panel's trap loses more marks than any other unit mistake in school physics. A prefix is glued to its unit: raise the unit to a power and the prefix's power of ten is raised with it:

1\ \mathrm{km^2} = (10^3\ \mathrm{m})^2 = 10^6\ \mathrm{m^2}, \qquad 1\ \mathrm{cm^3} = (10^{-2}\ \mathrm{m})^3 = 10^{-6}\ \mathrm{m^3} \qquad (3)

where: the exponent acts on everything inside the bracket — number and unit alike. Read $\mathrm{km^2}$ as "(kilometre) squared", never "kilo-(metre squared)": a square kilometre is a 1000-row grid of 1000 one-metre tiles. The same rule powers every density conversion: $1\ \mathrm{g/cm^3} = 10^{-3}\ \mathrm{kg}/10^{-6}\ \mathrm{m^3} = 10^3\ \mathrm{kg/m^3}$ — why water is both $1\ \mathrm{g/cm^3}$ and $1000\ \mathrm{kg/m^3}$ .

Changing units without changing physics

A measurement is a number times a unit, and the physical quantity is the whole product: $1.5\ \mathrm{m}$ and $150\ \mathrm{cm}$ are the same fact. That invariance is a see-saw —

Q = n_1 u_1 = n_2 u_2 \quad\Longrightarrow\quad n_2 = n_1\,\frac{u_1}{u_2} \qquad (4)

where: $Q$ — the physical quantity itself; $n_1, n_2$ — the numerical values; $u_1, u_2$ — the unit sizes. The number is inversely proportional to the unit's size: pick a unit 100 times smaller and the number grows 100-fold. Every conversion you have ever done is equation (4) in different clothes — and JEE-Main dresses it in its favourite costume, the "new system of units" problem, dispatched in the derivation below.

Go deeper · Derivation B · 1 minThe magnitude-conversion rule for any new system of units

Derivation BThe magnitude-conversion rule for any new system of units

We want a single formula converting the numerical value of any quantity between unit systems — SI to CGS, or to an invented exam system where "the unit of length is 10 cm and the unit of mass is 100 g". The strategy: write the quantity's unit as a product of powers of the mass, length and time base units, then apply the see-saw $n_1u_1 = n_2u_2$ to each base unit separately. Watch the exponents — each ratio gets raised to that unit's power, which is exactly where careless solutions die.

Step 1. Let the quantity's unit be built from base units as $u = M^{\beta} L^{\alpha} T^{\gamma}$ (for density: $\beta = 1$ , $\alpha = -3$ , $\gamma = 0$ , since density is mass per volume).

Step 2. Write the invariance: $Q = n_1\,M_1^{\beta} L_1^{\alpha} T_1^{\gamma} = n_2\,M_2^{\beta} L_2^{\alpha} T_2^{\gamma}$ , with subscript 1 the old base-unit sizes, 2 the new.

Step 3. Solve for the new numerical value:

n_2 = n_1 \left(\frac{M_1}{M_2}\right)^{\beta} \left(\frac{L_1}{L_2}\right)^{\alpha} \left(\frac{T_1}{T_2}\right)^{\gamma}

Each bracket is "old unit over new unit", raised to the quantity's exponent for that base. Why old-over-new: if the new mass unit is bigger, fewer of them are needed, so the ratio must shrink $n$ — the see-saw again, once per base unit.

Step 4. Test on a hand-checkable case: the newton in CGS. Force has $\beta=1, \alpha=1, \gamma=-2$ ; from (kg, m, s) to (g, cm, s): $n_2 = 1 \times (10^3)^1 \times (10^2)^1 \times 1 = 10^5$ . So $1\ \mathrm{N} = 10^5$ dyne — the textbook value. Verified: $10^3 \times 10^2 = 10^5$ ; cross-checked against the definition $1\ \mathrm{dyn} = 1\ \mathrm{g\,cm\,s^{-2}}$ and $1\ \mathrm{N} = 1\ \mathrm{kg\,m\,s^{-2}} = (10^3\,\mathrm{g})(10^2\,\mathrm{cm})\,\mathrm{s^{-2}} = 10^5\ \mathrm{g\,cm\,s^{-2}}$ .

One final structural fact. The SI is a coherent system: derived units are products of base units with no numerical factor — one newton is exactly $1\ \mathrm{kg\,m\,s^{-2}}$ . That is why formulas work in SI without conversion constants, why the next module (Derived Units & Unit Conversion) can build the whole zoo of newtons, joules and pascals from today's seven cards — and why "SI in, SI out" is law: feed a formula grams or centimetres and you have silently left the coherent system.

Limiting cases

Case	Result	Meaning
pure number (refractive index, strain)	no unit at all	ratios are identical in every unit system
prefix with $n = 0$	the bare unit	the base unit itself sits on the prefix ladder
unit made smaller	number grows in exact proportion	$n \times u$ is invariant — the see-saw of equation (4)
accepted non-SI units (min, h, L, eV)	fixed SI equivalents	convenient labels; convert before any formula
CGS system	same physics, shifted numbers: $1\ \mathrm{N} = 10^5$ dyn	unit systems are human conventions; nature ignores them

The second row is worth a pause: prefix arithmetic never touches the physics — it only slides the decimal point. If the slide changes your answer's physics (a car at $2\times10^7\ \mathrm{m/s}$ , a person massing $65\,000$ kg), the bookkeeping — not nature — has failed.

Worked examples

Board level — copper density and a speeding car (CBSE/ICSE/IGCSE pattern)

(a) Copper has density $8.96\ \mathrm{g/cm^3}$ ; express it in SI units. (b) Express $72\ \mathrm{km/h}$ in $\mathrm{m/s}$ .

Step 1. (a) Replace each prefixed unit by its power of ten: $1\ \mathrm{g} = 10^{-3}\ \mathrm{kg}$ , $1\ \mathrm{cm} = 10^{-2}\ \mathrm{m}$ .

Step 2. Cube where the unit is cubed — the trap: $1\ \mathrm{cm^3} = (10^{-2}\ \mathrm{m})^3 = 10^{-6}\ \mathrm{m^3}$ .

Step 3. Assemble: $8.96\ \mathrm{g/cm^3} = \dfrac{8.96 \times 10^{-3}\ \mathrm{kg}}{10^{-6}\ \mathrm{m^3}} = 8.96 \times 10^{3}\ \mathrm{kg/m^3}$ , so $\boxed{\rho = 8960\ \mathrm{kg/m^3}}$ . Sanity: water is $1\ \mathrm{g/cm^3} = 1000\ \mathrm{kg/m^3}$ ; copper is rightly nine times denser.

Step 4. (b) Convert each unit in the ratio: $72\ \mathrm{km/h} = \dfrac{72 \times 1000\ \mathrm{m}}{3600\ \mathrm{s}} = 72 \times \dfrac{5}{18} = \boxed{20\ \mathrm{m/s}}$ .

Step 5. The sentence worth a mark on board papers: "the numerical value changed because the unit changed; the physical quantity did not" — $n_1u_1 = n_2u_2$ in words.

Competitive level — density in an invented unit system (JEE-Main pattern)

The density of a material in the CGS system is $4\ \mathrm{g/cm^3}$ . In a system of units in which the unit of length is 10 cm and the unit of mass is 100 g, the density of the same material is:

Step 1. Identify the exponents for density: $\beta = 1$ (mass), $\alpha = -3$ (length), $\gamma = 0$ (time plays no role).

Step 2. Apply the conversion rule with old units (g, cm) and new units (100 g, 10 cm):

n_2 = 4 \times \left(\frac{1\ \mathrm{g}}{100\ \mathrm{g}}\right)^{1} \times \left(\frac{1\ \mathrm{cm}}{10\ \mathrm{cm}}\right)^{-3}

Step 3. Evaluate each bracket: mass ratio $= 10^{-2}$ ; length ratio $= 10^{-1}$ , and raised to $-3$ it becomes $10^{+3}$ .

Step 4. Multiply: $n_2 = 4 \times 10^{-2} \times 10^{3} = \boxed{40\ \text{new units}}$ .

Step 5. Sense-check without the formula: the new mass unit is 100 times bigger (number shrinks by 100); the new volume unit is $10^3$ times bigger (more mass per unit volume — number grows by 1000). Net $\times 10$ : $4 \to 40$ . ✓ Timing note: 60–90 seconds. Write the three brackets straight from $M^1L^{-3}$ — the only thinking is the sign of each exponent; sign slips here are the classic wrong-option generators.

Exam traps

Squared and cubed prefixes. $1\ \mathrm{km^2} = 10^6\ \mathrm{m^2}$ , not $10^3$ ; $1\ \mathrm{cm^2} = 10^{-4}\ \mathrm{m^2}$ ; $1\ \mathrm{mm^3} = 10^{-9}\ \mathrm{m^3}$ . This single slip explains most lost unit marks on IGCSE and CBSE numericals.

Grams smuggled into SI formulas. Mass 200 g means $m = 0.2$ in $\tfrac12mv^2$ , $F = ma$ , $p = mv$ . The tell: everyday objects with energies in thousands of joules.

Unit-symbol grammar — boards do mark it. Symbols are case-sensitive and never pluralised: kg (not Kg or kgs), s (not sec), K (not °K — the degree sign died in 1967), km/h (not kmph). Capital first letters are reserved for units named after people — N, J, W, Pa, A, K, Hz — while the spelled-out names stay lowercase: "newton", "joule". Writing "Kg" in a CBSE practical or "sec" on an ISC paper invites a deducted mark.

Non-SI intruders. Litre, hour, minute, electronvolt and tonne are accepted for use with the SI, not part of it: $1\ \mathrm{L} = 10^{-3}\ \mathrm{m^3}$ , $1\ \mathrm{h} = 3600\ \mathrm{s}$ , $1\ \mathrm{eV} = 1.6\times10^{-19}\ \mathrm{J}$ . Convert them before substituting into formulas.

km/h ↔ m/s factor inversion. $\times\frac{5}{18}$ going to m/s, $\times\frac{18}{5}$ back. Anchor: $36\ \mathrm{km/h} = 10\ \mathrm{m/s}$ . If your converted car outruns a jet, you multiplied the wrong way.

"Define the second/metre/kilogram" — the modern answers. Second via the caesium-133 frequency, metre via the fixed speed of light, kilogram via the fixed Planck constant. The Paris-artefact answer now loses the definition mark on CBSE and ICSE papers.

Origins · 1 minMax Planck and how this was discovered

Max Planck

1858–1947 · Berlin

In 1899 — a year before the quantum — Planck noticed that his new constant $h$ , together with $c$ and $G$ , could define units of length, mass and time "independent of special bodies and substances, valid for all times and all cultures, even extraterrestrial ones." It was a physicist's rebuke to a metrology of platinum cylinders in vaults: nature already provides the standards, if only our instruments can reach them. It took 120 years. In 2019 the kilogram — the last artefact unit in science — was redefined by fixing the exact value of Planck's own constant, making his "units for all times and all cultures" the literal law of world measurement. Every balance on Earth now traces, through the Kibble balance's electrical watts, to the constant that carries his name.

History

1875

— The Metre Convention: 17 nations found the BIPM and agree to share physical standards of the metre and kilogram.

1960

— The 11th CGPM names the Système International (SI) with six base units; the metre is redefined via a krypton wavelength.

1967

— The second is redefined by the caesium-133 hyperfine transition: atomic time replaces astronomical time.

1983

— The metre is redefined by fixing

c = 299\,792\,458

m/s exactly — length becomes a measurement of time.

2019

— All seven base units become constants-based; the kilogram is fixed via the Planck constant and Le Grand K retires to being merely an object.

Going further

Texts. NCERT Physics Part 1, Ch. 1 — the CBSE/JEE canonical statement · SI Brochure, 9th ed. (BIPM, 2019) — the primary source for all seven definitions, free online · CIE 9702 AS Topic 1 and CIE 0625 §1.1 · IB Physics guide (2025), Tool 3: "apply and use SI prefixes and units".

Provenance. Definitions and constant values per the BIPM SI Brochure (9th ed.). A verifier should recompute: $0.30/(2.998\times10^8) = 1.0\times10^{-9}$ s; $10/(2.998\times10^8) = 3.34\times10^{-8}$ s; $8.96\ \mathrm{g/cm^3} \to 8.96\times10^{-3}/10^{-6} = 8960\ \mathrm{kg/m^3}$ ; $72\ \mathrm{km/h} = 72\times1000/3600 = 20\ \mathrm{m/s}$ ; $1\ \mathrm{N} = (10^3)(10^2) = 10^5$ dyn; new-units density $4\times10^{-2}\times10^{3} = 40$ .

Prerequisites. Physical Quantities & Measurement. Leads to. Derived Units & Unit Conversion · Dimensions & Dimensional Formulae.

Why is the kilogram — and not the gram — the base unit?

Practicality frozen into history. The 1795 metric plan did centre on the gram (the mass of a cubic centimetre of water), but a one-gram standard is a fleck of metal — hopeless to machine and compare precisely. So the standard was built at a thousand grams, and that object's size became the base unit. We live with the oddity: the only base unit containing a prefix. Consequence: prefixes attach to gram ( $\mathrm{mg}, \mathrm{\mu g}$ ), never to kilogram, and formulas still demand mass in kg.

What happens to Le Grand K now — is it wrong?

Neither wrong nor a standard — just a beautifully made cylinder whose mass is now measured like anyone else's: about $1\ \mathrm{kg}$ with an uncertainty, instead of exactly $1\ \mathrm{kg}$ by decree. Before 2019 the sentence "Le Grand K has lost mass" was logically impossible — it was the kilogram, so the rest of the universe had gained — precisely the absurdity that forced the redefinition. It stays in its vault as a check standard: comparisons against Kibble-balance kilograms will finally reveal how much the artefact drifts.

Is the litre an SI unit? Can I use it in formulas?

The litre is a non-SI unit accepted for use with the SI: exactly $1\ \mathrm{L} = 10^{-3}\ \mathrm{m^3}$ (a 10 cm cube), but outside the coherent system — as are the minute, hour, day, tonne and electronvolt. Fine for stating quantities; convert to $\mathrm{m^3}$ , seconds and joules before substituting into formulas, because coherence guarantees formulas work only in pure SI. Worth memorising: a litre of water is 1 kg.

Do I need to memorise the exact values of the seven defining constants?

Know all seven pairings (which constant defines which unit) and a few values: $c = 3\times10^8\ \mathrm{m/s}$ (exactly $299\,792\,458$ ), plus the flavour of $h \approx 6.63\times10^{-34}\ \mathrm{J\,s}$ and $N_A \approx 6.022\times10^{23}\ \mathrm{mol^{-1}}$ . CBSE and ICSE ask "the kilogram is defined by fixing which constant?" as a one-marker; JEE and NEET supply constants; IB and A-Level print them in the data booklet. Nobody expects $9\,192\,631\,770$ from memory — but recognising it as "the caesium second" saves elimination time.

Why does electric current get a base unit when charge seems more fundamental?

A historical-practical choice, not a physical necessity. When the ampere joined the system, current was what laboratories could measure superbly (current balances measuring forces between coils), while counting individual charges was science fiction. Base-unit status follows measurability; the coulomb is happily derived, $1\ \mathrm{C} = 1\ \mathrm{A\,s}$ . Since 2019 the definition runs through charge anyway — the ampere carries $1/(1.602\,176\,634\times10^{-19})$ charges per second — but keeps the chair. Moral: which quantities are "base" is convention; the physics lives in the constants.

Why is the second defined by such an ugly number of oscillations?

Continuity beat elegance. When atomic clocks made caesium the new standard in 1967, metrologists measured its frequency in the old astronomical second as precisely as possible — the answer was $9\,192\,631\,770$ cycles. Freezing exactly that number meant the new second matched the old seamlessly: no calendar jumped. The trick repeated in 1983 ( $c$ frozen at its best-measured value) and 2019 ( $h$ frozen with its measured decimals). Redefinitions are designed to be invisible — units never change size, only their anchors change.