The Metric System
Theory
The metric system measures length in metres, mass in grams and capacity in litres. A prefix such as kilo (\(1000\)), centi (one hundredth) or milli (one thousandth) tells you how big the unit is. This Year 7 maths page shows the conversion charts and how to change between units.
kilo means \(1000\): \(1\) km \(= 1000\) m. centi means one hundredth: \(100\) cm \(= 1\) m. milli means one thousandth: \(1000\) mL \(= 1\) L. mega means one million: \(1\) ML \(= 1000\) kL \(= 1\,000\,000\) L. A tonne (t) is \(1000\) kg.
Bigger unit to smaller unit: multiply. A bigger unit needs more of the smaller unit: \(3\) kg \(= 3 \times 1000 = 3000\) g.
Smaller unit to bigger unit: divide. A smaller unit makes fewer of the bigger unit: \(70\) mm \(= 70 \div 10 = 7\) cm.
No single arrow? Take two steps on the chart (m to cm to mm), or join the steps: \(1\) m \(= 100 \times 10\) mm \(= 1000\) mm.
Time is not metric: \(1\) day \(= 24\) h, \(1\) h \(= 60\) min, \(1\) min \(= 60\) s.
Choose a sensible unit, one that gives an easy-to-read number: a pencil is about \(18\) cm, a bag of rice \(2\) kg, a dose of medicine \(5\) mL and a loaded truck \(12\) t.
Facts to know:
| Length | Mass | Capacity | Time |
|---|---|---|---|
| \(1\) km \(= 1000\) m | \(1\) t \(= 1000\) kg | \(1\) ML \(= 1000\) kL | \(1\) day \(= 24\) h |
| \(1\) m \(= 100\) cm | \(1\) kg \(= 1000\) g | \(1\) kL \(= 1000\) L | \(1\) h \(= 60\) min |
| \(1\) cm \(= 10\) mm | \(1\) g \(= 1000\) mg | \(1\) L \(= 1000\) mL | \(1\) min \(= 60\) s |
| \(1\) m \(= 1000\) mm |
How to convert a measurement
- Find the two units on the chart.
- Decide: to a smaller unit, multiply; to a bigger unit, divide.
- Use the factor on each arrow (two steps if needed).
- Check: smaller unit, bigger number.
(i) \(2.5\) L to mL
(ii) \(3.2\) km to m
(iii) \(1.6\) g to mg
| \(2.5 \times 1000\) | \(=\) | \(2500\) |
| \(3.2 \times 1000\) | \(=\) | \(3200\) |
| \(1.6 \times 1000\) | \(=\) | \(1600\) |
(i) \(2500\) mL
(ii) \(3200\) m
(iii) \(1600\) mg
(i) \(240\) mL to L
(ii) \(420\) m to km
(iii) \(38\) m to km
| \(240 \div 1000\) | \(=\) | \(0.24\) |
| \(420 \div 1000\) | \(=\) | \(0.42\) |
| \(38 \div 1000\) | \(=\) | \(0.038\) |
(i) \(0.24\) L
(ii) \(0.42\) km
(iii) \(0.038\) km (the \(0\) after the point holds the place)
| \(2.3 \times 1000\) | \(=\) | \(2300\) |
| \(2300 \times 100\) | \(=\) | \(230\,000\) |
km to m, then m to cm: \(230\,000\) cm. In one step: \(1\) km \(= 100\,000\) cm, and \(2.3 \times 100\,000 = 230\,000\).
| \(0.85 \times 1000\) | \(=\) | \(850\) |
| \(82 \times 10\) | \(=\) | \(820\) |
In mm: \(820\), \(845\), \(850\). So \(82\) cm, \(845\) mm, \(0.85\) m.
| \(12 \times 1000\) | \(=\) | \(12\,000\) |
| \(45 \times 250\) | \(=\) | \(11\,250\) |
| \(12\,000 - 11\,250\) | \(=\) | \(750\) |
| \(750 \div 1000\) | \(=\) | \(0.75\) |
\(0.75\) L is left.
| \(4.5 \times 1000\) | \(=\) | \(4500\) |
| \(4500 \div 9\) | \(=\) | \(500\) |
\(500\) buckets
(i) the mass of a bus
(ii) the thickness of a coin
(iii) a spoonful of medicine
(i) tonnes (t)
(ii) millimetres (mm)
(iii) millilitres (mL)
Common pitfalls
Frequently asked questions
How many grams are in a kilogram?
\(1000\).
How do you change centimetres to millimetres?
Multiply by \(10\). \(8.6\) cm \(= 86\) mm.
How do you change metres to kilometres?
Divide by \(1000\). \(420\) m \(= 0.42\) km.
What does milli mean?
One thousandth. \(1\) mL is one thousandth of a litre.
How many litres are in a kilolitre?
\(1000\).