MYP 1 Mathematics · Geometry

Unit conversions — length, mass and volume

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Why Do We Need Units of Measurement?

Imagine trying to buy fabric from a market where every seller uses a different word for 'one metre' — chaos! Throughout history, people used their own local systems of measurement, making trade, construction, and science incredibly difficult.

By the 19th century, the world needed a common language for measurement. The solution was the metric system — a universal set of units based on powers of 10, making it logical, consistent, and easy to convert between units. When calculating the perimeter of a shape or the volume of a container, all measurements must be in the same unit — that's why conversions matter in geometry too!

The three most important quantities in the metric system and their common units are:

  • Metres (m) — for measuring length (the SI base unit is also the metre)
  • Grams (g) — for measuring mass (note: the official SI base unit is the kilogram, kg, but we use grams as our starting point for learning prefixes)
  • Litres (L) — for measuring volume of liquids (note: the SI base unit for volume is actually the cubic metre, m³, but litres are widely used in everyday science)
Analogy

Think of the metric system like money. If you know that 100 cents = 1 dollar, you can quickly convert any amount. The metric system works the same way — every unit is related by a factor of 10.

Metric Prefixes — The Building Blocks

The metric system uses prefixes added to the base unit to create larger or smaller units. Each prefix represents a specific power of 10.

Here are the most important prefixes, from largest to smallest:

PrefixSymbolMeaningExample
kilo-k× 1000kilometre (km)
hecto-h× 100hectometre (hm)
deca-da× 10decametre (dam)
(base unit)m / g / L× 1metre, gram, litre
deci-d× 0.1 (÷ 10)decimetre (dm)
centi-c× 0.01 (÷ 100)centimetre (cm)
milli-m× 0.001 (÷ 1000)millimetre (mm)
Prefix

A prefix is a word part added to the beginning of a unit name that changes its size by a specific power of 10.

Exam Tip

A popular memory phrase for the prefixes in order is: King Henry Died Mostly Drinking Cold Milk — standing for kilo, hecto, deca, (base), deci, centi, milli.

Note

Focus on these four first! In everyday science, the prefixes you will use most often are kilo-, the base unit, centi-, and milli-. Hecto- and deca- are included in the table for completeness, but you will rarely encounter them in science or daily life — so don't worry about memorising them right away.

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