Metric units and conversions: QCE Essential Mathematics Unit 3
“Use metric units of length, mass and capacity, convert between them, choose appropriate units and levels of accuracy, and calculate with measurements in practical contexts”
Convert metric units by multiplying when changing to a smaller unit and dividing when changing to a bigger unit (10, 100 or 1000). Remember 1 cm³ = 1 mL and 1 m³ = 1000 L. Put all measurements in the same unit before calculating, round sensibly for the context, and check your answer is reasonable.
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What this dot point is asking
Measurement questions in Essential Mathematics almost always involve units. You need to choose sensible metric units, convert between them accurately, and keep track of units through a calculation. This is core subject matter for the Unit 3 common internal assessment (CIA).
The answer
The metric prefixes
| Prefix | Meaning | Example |
|---|---|---|
| kilo (k) | 1000 times | 1 km = 1000 m |
| centi (c) | one hundredth | 1 m = 100 cm |
| milli (m) | one thousandth | 1 m = 1000 mm, 1 L = 1000 mL |
Mass also uses the tonne: 1 t = 1000 kg.
- Bigger unit to smaller unit: multiply (m to cm: times 100).
- Smaller unit to bigger unit: divide (mL to L: divide by 1000).
- Length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
- Mass: 1000 mg = 1 g, 1000 g = 1 kg, 1000 kg = 1 t.
- Capacity: 1000 mL = 1 L, 1000 L = 1 kL.
- Volume and capacity: 1 cm³ = 1 mL, 1 m³ = 1000 L.
Choosing units and accuracy
Choose units that suit the size of the object: millimetres for screws, metres for rooms, kilometres for distances between towns. Round answers to a sensible accuracy for the context: a carpenter may need millimetres, but a road trip only needs kilometres. When an answer is a number of whole items (tiles, trips, bags), round up if you need enough to finish the job.
Checking reasonableness
Estimate first with rounded numbers, then compare with your calculated answer. If a kitchen bench comes out at 250 m long, you have probably forgotten to convert centimetres.
A water tank holds 5.4 kL. A household uses 180 L per day. How many full days will a full tank last?
- Convert to the same unit: 5.4 kL = 5400 L.
- Divide: 5400 divided by 180 = 30.
- Answer: 30 days.
- Check: about 5000 L divided by about 200 L per day is about 25 days, so 30 is reasonable.
- Multiplying when you should divide
- Ask: is the new unit smaller (more of them) or bigger (fewer of them)?
- Mixing units in one calculation
- Convert everything to the same unit before adding or multiplying.
- Rounding down when you need enough
- 3.2 bags of cement means buying 4 bags.
Practice questions
Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.
foundation3 marksA builder needs 4 lengths of timber: 1.2 m, 850 mm, 95 cm and 2.05 m. Find the total length in metres.Show worked solution →
Convert everything to metres first:
- 1.2 m
- 850 mm = 0.85 m
- 95 cm = 0.95 m
- 2.05 m
Total = 1.2 + 0.85 + 0.95 + 2.05 = 5.05 m.
Marking guide: 1 mark for converting mm to m, 1 mark for converting cm to m, 1 mark for the correct total with units.
core3 marksA recipe needs 375 mL of milk for one batch of pancakes. How many full batches can be made from a 2 L carton, and how much milk is left over?Show worked solution →
2 L = 2000 mL.
2000 divided by 375 = 5.33, so 5 full batches can be made.
Milk used = 5 times 375 = 1875 mL, so milk left over = 2000 minus 1875 = 125 mL.
Marking guide: 1 mark for converting litres to millilitres, 1 mark for 5 batches, 1 mark for 125 mL.
exam5 marksA landscaper orders gravel for three garden beds. Each bed needs 0.6 t. The trailer can carry at most 1500 kg per trip, and each trip costs 45 dollars. Gravel costs 62 dollars per tonne. Find the total cost of the gravel and the trips, and justify the number of trips.Show worked solution →
Total gravel = 3 times 0.6 t = 1.8 t = 1800 kg.
Trips: 1800 kg divided by 1500 kg = 1.2, so 2 trips are needed (one trip is not enough, and the trailer cannot carry a partial extra load in the same trip).
Gravel cost = 1.8 times $62 = $111.60.
Trip cost = 2 times $45 = $90.
Total = $201.60.
Reasonableness: about 2 tonnes at about $60 per tonne is about $120, plus two trips at about $50 is about $100, so about $220. The answer is reasonable.
Marking guide: 1 mark for 1800 kg, 1 mark for 2 trips with justification, 1 mark for gravel cost, 1 mark for trip cost, 1 mark for the total with a reasonableness check.