Intuition The one core ideaEvery measurement is a comparison to an agreed standard : a number tells you how many copies of that standard you have. All of chemistry's units are either base standards we simply agree on (mass, amount, temperature, time, length) or built standards made by clicking those together with multiply and divide.
This page is the toolbox. The parent note throws formulas and symbols at you and assumes you already know what every mark means. Here we earn every single mark from zero — starting from the idea of "a number with a name attached" and building up, in order, to everything the parent uses. By the end of this page you will be able to read a formula like the gas law or the mole relation without a single mystery symbol.
Definition Quantity, number, unitA quantity is anything you can measure. When you write it down you always get two parts glued together:
a number (how many), and
a unit (copies of what standard).
"5 apples 5
Figure s01 — Two identical "2"s, two different rulers. On the left, "2" counts small blue circles (a tiny amount of stuff); on the right, "2" counts big pink boxes (a huge amount). The number is the same but the amount is not, because the unit — the ruler you are counting — is different. Take-away: the number alone is meaningless; the unit tells you what you counted.
Intuition Why the unit can never be droppedLook at the figure: the same number 2 2 2 is the ruler; the number just counts rulers. This is exactly why chemistry insists everyone share one ruler set — the SI system.
We now define each mark the parent note uses. They are ordered so that nothing appears before the thing it is built from .
A variable is just a boxed-up number we haven't filled in yet — a placeholder. When we write m remind you what it stands for: m V T
Mnemonic Reading the alphabet soupMost symbols are the first letter of the English (or Latin) word : m ass, V olume, T emperature (Latin temperatura ), p ressure, n umber of moles, F orce, d istance, a cceleration, W ork.
Definition Exponent (superscript)A small raised number means repeated multiplication . Writing a 3 a × a × a
Positive: a 2 = a × a a 3 = a × a × a Negative: flips it into a division. a − 2 = a 2 1 Zero: a 0 = 1 always (an empty product — you multiplied nothing, which leaves the "do-nothing" number 1
Intuition What a zero power means for unitsa 0 = 1 m 0 1 vanishes . The quantity is then dimensionless (a pure number with no ruler attached), like n = N / N A
Intuition Why negatives instead of fractions?Writing units on one line with negative exponents is the same thing as a fraction, just laid flat. Scientists prefer it because you can read off every base brick and its count at a glance — no hunting above and below a fraction bar. (We can't show a real example yet — the units below are defined in section 2 — but the rule is: anything under the bar gets a minus sign.)
Definition Scientific notationA way to write very big or very small numbers without a parade of zeros. 6.022 × 1 0 23 6.022 23 1 0 − 3 3 = 0.001
Figure s02 — Anatomy of 6.022 × 1 0 23 6.022 × 1 0 23
Intuition Why chemists cannot live without itLook at the figure: writing Avogadro's number out longhand needs many digits. Atoms are absurdly numerous and absurdly light, so every chemical number is either enormous or minuscule. The × 1 0 n 6.022 scale (1 0 23 Significant Figures and Measurement Uncertainty — the front part is exactly the "significant" digits.
Worked example Reading the exponents
1 0 23 1 0 − 3 0.001 4 × 1 0 4 = 40000 101325 = 1.01325 × 1 0 5
A prefix is a short word stuck onto a unit to multiply it by a power of ten, so you don't write the × 1 0 n × 1 0 3 × 1 0 − 3
The table below shows only the handful this topic actually uses — it is a selective list, not the full set . The real SI prefix ladder runs much further in both directions (e.g. mega M = 1 0 6 G = 1 0 9 μ = 1 0 − 6 n = 1 0 − 9
prefix
symbol
means
kilo
k × 1 0 3
(none)
× 1 0 0 = 1
deci
d × 1 0 − 1
centi
c × 1 0 − 2
milli
m × 1 0 − 3
Intuition Why prefixes exist — and a warningThe prefix rides in front of a unit: km = 1 0 3 m cm = 1 0 − 2 m dm = 1 0 − 1 m 1 L = 1 dm 3 Warning: the "kilogram" is the one base unit that already has a prefix baked into its name — the base standard is the kilogram , not the gram. That is a historical quirk you simply memorise.
= ≈ ∝
= exactly equal .≈ approximately equal — we rounded (e.g. ≈ 1.00 × 1 0 5 ∝ proportional to . Precisely: A ∝ B fixed number k constant of proportionality ) such that A = k B
∝ A = k B A B straight line through the origin with slope k B A k ( 0 , 0 ) B = 0 A = 0 p , V T ∝ = k T T = 0 zero energy / zero motion — absolute zero. Celsius puts its zero at water's freezing point, so its line would not pass through the origin and the proportion breaks.
[ ⋅ ] [ X ] X [ F ] on the units alone , ignoring the numbers — the heart of Dimensional Analysis .
A base unit is a standard chosen independently — it isn't built from any other unit. You cannot derive it; the world's scientists simply agreed on a fixed reference.
The full SI system has seven base units. Two of them — the ampere (A and the candela (cd — do not appear anywhere in this topic, so we set them aside (they belong to electricity and to light measurement). That leaves the five this chapter actually leans on:
kg how heavy (mass).mol how many particles (amount).K how hot , from absolute zero (temperature).m how long (length; used to build volume and pressure).s how long in time (duration; hides inside energy and pressure via "per second squared").
Intuition Why the second sneaks in everywhereYou rarely see time in a chemistry formula, but it is buried in the derived units. Force involves acceleration — "how fast the speed changes each second" — so a s − 2 s s 2 s − 2
Figure s03 — The LEGO picture of units. On the left, five separate base bricks (kg, mol, K, m, s) — each an independently agreed standard. The arrow "combine" leads to the right, where those same bricks are snapped together to spell out the derived units: joule (kg m 2 s − 2 kg m − 1 s − 2 m 3 /1000
Intuition Base vs built — the LEGO pictureIn the figure, the base bricks sit on the left. On the right, bigger shapes (joule, pascal, litre) are those same bricks snapped together . No new material is introduced on the right — only new arrangements. That single idea is what "derived unit" means, and it's why you never memorise derived units: you read them off the arrangement (we prove this in section 3b).
Intuition "Mole" is to atoms what "dozen" is to eggsA dozen means 12 what you have 12 mole means 6.022 × 1 0 23 count that also ties to a weighable mass. See The Mole Concept .
N A N A N A = 6.022 × 1 0 23 A N
Now that every base brick (kg, mol, K, m, s) is defined, we can snap them together and read off the built units.
Worked example Unit-algebra in action (the promised worked steps)Q1 — is 2 1 m v 2 Speed v m s − 1 ( m s − 1 ) 2 = m 2 s − 2 kg ⋅ m 2 s − 2 = kg m 2 s − 2 = J ✓ 2 1 = 1
Q2 — check p = F / A m 2 kg m s − 2 m 1 m 2 m 1 − 2 = m − 1 kg m − 1 s − 2 = Pa ✓
Q3 — watch a unit vanish. In n = N / N A N = 1 N A mol − 1 mol − 1 1 = mol 1 = mol count 0 = 1
The diagram below is a dependency chart : read every arrow as "you must understand the box it starts from before the box it points to makes sense." Trace any path from top to bottom and you retrace the exact build order of this page — from "a number plus a unit" at the very top, through exponents, prefixes and base bricks, into the derived units and the mole trio, and finally into the parent topic at the bottom, which consumes all of them.
mole trio n equals m over M
SI units in chemistry topic
The topic (the parent, also in Hinglish ) sits at the bottom because it consumes all of these.
Cover the answers and test yourself — you're ready when all reveal green.
A measurement has two glued parts — name them a number and a unit
What does the exponent in s − 2 divide by s × s
What is a 0 a 0 = 1
Write 101325 1.01325 × 1 0 5
What does the prefix "kilo" multiply a unit by? "milli"? kilo = × 1 0 3 = × 1 0 − 3
Which base unit already contains a prefix in its name the kilogram (the base standard is the kilogram, not the gram)
What does [ F ] "the units of force"
Difference between a base unit and a derived unit base is an agreed independent standard; derived is base units multiplied/divided
How many base units does the full SI system have, and which two does this topic ignore seven; the ampere (current) and the candela (brightness) are unused here
State A ∝ B there is a fixed constant k A = k B
Why must T p V = n R T energy ∝ T T = 0
Derive the newton from base units F = ma ⇒ kg ⋅ m s − 2
Express the joule in base units kg m 2 s − 2
Express the pascal in base units kg m − 1 s − 2
How many m³ in 1 L 1 0 − 3 m 3
What is N A Avogadro's number, 6.022 × 1 0 23
Which of n , N , N A N
Read off the units of M n = m / M mass per mole, g/mol (or kg/mol)
