Standard units, conversions, and time arithmetic
This is one of those topics where dropping a single zero, or treating time like base-10, costs marks. Be methodical.
Length (metric)
1 km = 1000 m. 1 m = 100 cm. 1 cm = 10 mm. So 1 m = 1000 mm and 1 km = 100,000 cm = 1,000,000 mm.
To convert downwards (km → m → cm → mm), multiply by 1000, 100, 10. To go upwards, divide.
Worked example: 2.4 km in cm.
- 2.4 km × 1000 = 2400 m.
- 2400 m × 100 = 240,000 cm.
Mass
1 t (tonne) = 1000 kg. 1 kg = 1000 g. 1 g = 1000 mg.
So 2.5 kg = 2500 g; 6700 mg = 6.7 g; 0.4 t = 400 kg.
Volume / capacity
1 l (litre) = 1000 ml. 1 ml = 1 cm³. So 1 l = 1000 cm³.
For larger volumes: 1 m³ = 1,000,000 cm³ = 1000 l.
Money
In the UK, £1 = 100p. To go between £ and pence, multiply or divide by 100.
When working with money, always quote answers to 2 decimal places (in pounds) unless told otherwise. £14 → £14.00 in a final answer is fine.
Time — the base-60 trap
This is where students lose marks most often.
- 1 minute = 60 seconds.
- 1 hour = 60 minutes = 3600 seconds.
- 1 day = 24 hours.
You cannot enter 1 hr 45 min directly into a calculator as 1.45. Convert first:
- 45 min as a fraction of an hour = 45/60 = 0.75.
- So 1 hr 45 min = 1.75 hours.
Conversely, 2.4 hours = 2 hr + 0.4 × 60 min = 2 hr 24 min, not 2 hr 40 min.
Time arithmetic
For finding the duration between two times, don't subtract digits as if they were decimals.
Worked example: from 10:35 to 13:18 — how long?
- 10:35 → 13:35 is 3 hours.
- 13:35 → 13:18 is back 17 min, so subtract: 3 hr − 17 min = 2 hr 43 min.
- Or directly: count up: 10:35 → 11:00 (25 min), 11:00 → 13:00 (2 h), 13:00 → 13:18 (18 min). Total: 25 + 18 + 120 = 163 min = 2 hr 43 min.
Imperial-to-metric (memorise the basics)
Foundation tier may need:
- 1 inch ≈ 2.54 cm.
- 1 foot = 12 inches.
- 1 mile ≈ 1.6 km (so 5 miles ≈ 8 km).
- 1 kg ≈ 2.2 pounds.
- 1 litre ≈ 1.75 pints; 1 gallon ≈ 4.5 litres.
Speed–distance–time
Speed = Distance / Time. Distance = Speed × Time. Time = Distance / Speed.
Units must be consistent. mph and miles → fine. mph and km → convert one of them first.
Worked example: a car travels 75 miles in 1 hr 30 min. Find its average speed.
- 1 hr 30 min = 1.5 hr.
- 75 ÷ 1.5 = 50 mph.
⚠Common mistakes— Common mistakes (examiner traps)
- Treating time as decimal. 2 hr 40 min ≠ 2.40 hr; it's 2 + 40/60 = 2.667 hr.
- Confusing cm² and cm. Squared/cubed units convert by 100² and 100³, not 100.
- Forgetting £ → p uses ×100. Easy mark to lose: £4.50 = 450p.
- Mixing units in a formula. Speed in km/h with time in seconds gives nonsense.
- 24-hour vs 12-hour confusion. Read carefully whether the question is using a.m./p.m.
➜Try this— Quick check
(a) 4.2 m in mm = ? (b) 2 hr 15 min as a decimal in hours = ? (c) A train covers 360 km in 4 hours. Average speed?
Answers: (a) 4200 mm; (b) 2.25 hr; (c) 90 km/h.
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