The Metric System
The metric system measures length in metres, mass in grams and capacity in litres, with prefixes such as kilo, centi and milli showing the size of each unit. This NSW Year 7 maths subtopic consolidates primary-school skills and has no Stage 4 outcome of its own, but every later measurement topic depends on it.
You will convert units by multiplying when you change to a smaller unit and dividing when you change to a larger one, take two steps when needed, choose a sensible unit and change to one unit before comparing or adding. Think rope lengths, flour for a recipe or a rainwater tank in kilolitres. It is part of Year 7 Area and Volume.
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?
\(1000\).