MISSION · Measurement
Mass and Capacity
The same prefixes, doing the same job on different quantities
LEVEL 1 · EXPLORE
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LEVEL 2 · LEARN
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The idea in one sentence
Mass and capacity use the very same metric prefixes as length, so if you can convert centimetres you can already convert millilitres.
One set of prefixes, three quantities
Milli means a thousandth. Centi means a hundredth. Kilo means a thousand.
\[1000 \text{ g} = 1 \text{ kg} \qquad 1000 \text{ mg} = 1 \text{ g} \qquad 1000 \text{ kg} = 1 \text{ tonne}\] \[1000 \text{ ml} = 1 \text{ litre} \qquad 100 \text{ cl} = 1 \text{ litre}\]That is the whole system. Learn the prefixes once and they apply to length, mass, and capacity identically — which is exactly what the metric system was designed for, and what the older units it replaced could not do.
Which unit for which job
| Quantity | Unit | Roughly |
|---|---|---|
| Mass | milligram | a grain of salt |
| gram | a paperclip | |
| kilogram | a bag of sugar | |
| tonne | a small car | |
| Capacity | millilitre | a teaspoon is about 5 |
| litre | a large bottle of drink |
Choosing sensibly matters as much as converting correctly. A person’s mass in milligrams is technically right and completely unreadable.
The direction rule, again
Same as every conversion: to a smaller unit, multiply; to a bigger unit, divide.
2.5 kg is \(2.5 \times 1000 = 2500\) g, because grams are smaller and it takes more of them. 750 ml is \(750 \div 1000 = 0.75\) litres.
Check the answer against common sense each time. A bag of flour is about 1.5 kg; if your working says 1500 kg, you multiplied when you should have divided.
The link between capacity and volume
Capacity is how much a container holds, and it connects directly to the space inside it:
\[1 \text{ ml} = 1 \text{ cm}^3 \qquad 1 \text{ litre} = 1000 \text{ cm}^3\]So a box measuring 10 cm by 10 cm by 10 cm holds exactly one litre. That is not a coincidence — the litre was defined that way. Water was then used to link mass to it, so one litre of water has a mass of about one kilogram, and a millilitre about a gram.
Those three facts together — a cube of side 10 cm, one litre, one kilogram of water — are worth remembering as a single picture.
Mass and weight
In everyday speech they’re used interchangeably. In physics they differ: mass is how much matter there is, measured in kilograms and unchanged wherever you go. Weight is the force of gravity pulling on that mass, measured in newtons, and it is six times smaller on the Moon.
An astronaut’s mass does not change in orbit; their weight does.
Common mix-ups
- Dividing when you should multiply. Smaller unit, bigger number.
- Miscounting the zeros. Kilo to milli is two steps — a million, not a thousand.
- Adding across units. Convert to one unit before adding.
- Writing 1.5 kg as “1 kg 5 g”. It’s 1 kg 500 g, because the .5 is half a kilogram.
Check yourself
A recipe needs 250 g of flour and you have a 2 kg bag. How many batches can you make? And how many 330 ml cans fill a 2 litre jug?
\(2 \text{ kg} = 2000\) g, and \(2000 \div 250 = 8\) batches. For the cans, \(2000 \div 330 \approx 6.06\), so 6 full cans with a little room left.
LEVEL 3 · REFLECT
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