Units & measurement · 16 pages
Units & measurement
Clear, standards-grounded explainers for how we measure the world — the seven SI base units and their 2019 redefinition, the metric system and its prefixes, unit conversion, scientific notation, and the ideas of accuracy, precision and uncertainty. Each page leads with a concise definition and links across to the wider CASRAI standards and dictionary.
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All 16 units & measurement pages
Metric vs imperial
The difference is that the metric system is a decimal (base-10) system built on the International System of Units (SI), where units differ by powers of ten. The imperial system uses traditional British units — feet, pounds, stones, pints — with irregular conversions. Almost every country now uses metric; the United States is the main exception.
ComparisonWeight vs mass
The difference is that mass is the amount of matter in an object — a fixed property measured in kilograms that does not change with location. Weight is the force gravity exerts on that mass, measured in newtons, and it varies with gravity. An astronaut’s mass is identical on the Moon, but their weight there is about one-sixth.
DefinitionSI base units
The SI base units are the seven fundamental units of the International System of Units: the second (time), metre (length), kilogram (mass), ampere (current), kelvin (temperature), mole (amount of substance) and candela (luminous intensity). Every other SI unit is built from these. Since the 2019 redefinition, each is defined by a fixed constant of nature, not a physical object.
DefinitionMetric system
The metric system is a decimal system of measurement in which units for the same quantity differ by powers of ten — a kilometre is 1,000 metres. Its modern, standardised form is the International System of Units (SI). Adopted in France in the 1790s, it is now the official system in almost every country and required throughout science.
DefinitionMetric prefixes
Metric prefixes are standard multipliers that attach to any SI unit to scale it by a power of ten. Kilo- means a thousand, centi- a hundredth, milli- a thousandth, mega- a million and micro- a millionth, so a kilometre is 1,000 metres. The same prefixes work with every unit, letting the metric system describe sizes from atoms to galaxies.
DefinitionUnit conversion
Unit conversion is the process of changing a measurement from one unit to another while keeping the actual quantity the same — for example, expressing 5 kilometres as 5,000 metres. It works by multiplying by a conversion factor: a ratio equal to one, such as 1,000 m / 1 km, that cancels the old unit and introduces the new one.
DefinitionDimensional analysis
Dimensional analysis is the method of tracking the units, or dimensions, of physical quantities through a calculation. By treating units as algebraic terms that multiply and cancel, it lets you convert between units and check that an equation is consistent. If the units on each side do not match, the equation must be wrong, whatever the numbers say.
DefinitionAccuracy and precision
Accuracy is how close a measurement is to the true value, while precision is how close repeated measurements are to each other. The two are independent: readings can be precise but inaccurate, or accurate but imprecise. The classic illustration is a dartboard — accuracy hits the bullseye, precision groups the darts tightly.
DefinitionMeasurement uncertainty
Measurement uncertainty is the quantified doubt that attaches to every measurement result — the range within which the true value is reasonably expected to lie. No measurement is ever exact, so a complete result has two parts: the measured value and its uncertainty, often written "100.0 ± 0.2 grams". It arises from random and systematic effects.
DefinitionSignificant figures
Significant figures are the digits in a measurement that carry meaningful information about its precision — all the certain digits plus the first uncertain one. In 0.00420, the significant figures are 4, 2 and 0, giving three; the leading zeros only mark the decimal place. Using the right number stops a result implying false precision.
DefinitionScientific notation
Scientific notation is a way of writing very large or very small numbers compactly, as a coefficient between 1 and 10 multiplied by a power of ten. The speed of light, 300,000,000 metres per second, becomes 3 × 10⁸; a wavelength of 0.0000005 metres becomes 5 × 10⁻⁷. The exponent counts how many places the decimal point moves.
DefinitionMass
Mass is the amount of matter in an object and a measure of how strongly it resists being accelerated. Its SI unit is the kilogram, and unlike weight it does not change with location: mass is identical on the Earth, the Moon or in space. It is the basis of weight (weight = mass × gravity).
DefinitionDensity
Density is the mass of a substance per unit of its volume — how much matter is packed into a given space. It is calculated as density = mass ÷ volume, with the SI unit kilograms per cubic metre. Density explains floating and sinking: an object less dense than water floats, one denser sinks. It is an intrinsic property.
DefinitionVolume
Volume is the amount of three-dimensional space that an object or substance occupies. Its SI unit is the cubic metre, though the litre and millilitre are widely used for liquids. It is calculated from dimensions for regular shapes — length × width × height for a box — and measured by displacement for irregular ones. It is a derived quantity.
DefinitionTemperature scales
Temperature scales are agreed systems for measuring how hot or cold something is. The three in common use are Celsius, where water freezes at 0 °C and boils at 100 °C; Fahrenheit, where these are 32 °F and 212 °F; and the kelvin, the SI base unit, which starts from absolute zero and has no negative values.
DefinitionAvogadro’s number
Avogadro’s number is the number of elementary entities — atoms, molecules or ions — in one mole of a substance, approximately 6.022 × 10²³. It links the invisible scale of atoms to laboratory quantities. Since the 2019 SI redefinition, the value is fixed exactly at 6.02214076 × 10²³ per mole, and it defines the mole itself.
