Module 3 of 8Lesson 1 of 6 · Units, Time & Timetables
Measure · Lesson 1 of 5

Units, Time & Timetables

🔵 CorePapers 1, 2 & 3
1 Learn it

Metric units — you must convert fluently:

MeasureConversions
Length1 cm = 10 mm · 1 m = 100 cm · 1 km = 1 000 m
Mass1 kg = 1 000 g · 1 tonne = 1 000 kg
Capacity1 litre = 1 000 ml · 1 litre = 1 000 cm³
Area1 m² = 10 000 cm² (because 100 × 100)
Volume1 m³ = 1 000 000 cm³ (because 100 × 100 × 100)
💡 Area and volume conversions square or cube the length factor. From m to cm you multiply lengths by 100, areas by 100² and volumes by 100³.

Time. 1 hour = 60 minutes — so 2.4 hours is 2 h 24 min, not 2 h 40 min. Convert decimals of an hour by multiplying by 60.

12-hour and 24-hour clocks: 2:35 pm = 14 35. Midnight is 00 00; noon is 12 00.

Timetables: read down the column for one bus/train; time differences are found by counting up to the next hour, then on — e.g. from 09 47 to 11 15 is 13 min (to 10 00) + 1 h 15 min = 1 h 28 min.

2 Watch it work
EXAMPLE 1 · Converting units

Convert (a) 3.6 km to m, (b) 2 500 g to kg, (c) 4.2 m² to cm².

(a) \(3.6\times1000 = 3\,600\) m.

(b) \(\dfrac{2500}{1000} = 2.5\) kg.

(c) \(4.2\times10\,000 = 42\,000\) cm².

EXAMPLE 2 · Time arithmetic

A film starts at 19 45 and lasts 2 hours 38 minutes. When does it end?

Step 1 — add the hours: 19 45 + 2 h = 21 45.

Step 2 — add the minutes: 21 45 + 38 min. 45 + 38 = 83 min = 1 h 23 min, so 21 45 + 1 h 23 min = 22 23.

Answer: 22 23 (10:23 pm).

EXAMPLE 3 · Timetable

Part of a bus timetable from Gaborone to Francistown:

Bus ABus B
Gaborone06 3008 15
Mahalapye08 5510 32
Palapye09 4011 18
Francistown11 5013 25

(a) How long does Bus A take from Mahalapye to Francistown? (b) Thabo arrives at the Gaborone rank at 07 10. How long does he wait for the next bus?

(a) 08 55 → 11 50: 1 h 5 min (to 10 00) + 1 h 50 min = 2 h 55 min.

(b) Next bus is Bus B at 08 15. Wait: 07 10 → 08 15 = 1 h 5 min.

3 Your turn
🚫 No calculator3 marks

Convert (a) 0.75 km to m, (b) 640 ml to litres, (c) 3 500 cm² to m².

Show solution

(a) \(0.75\times1000 = \mathbf{750\ m}\).

(b) \(\dfrac{640}{1000} = \mathbf{0.64\ litres}\).

(c) \(\dfrac{3500}{10\,000} = \mathbf{0.35\ m^2}\).

Why: for areas the factor is 10 000, not 100 — a square metre contains 100 × 100 small centimetre squares.

🚫 No calculator3 marks

A night bus leaves Maun at 21 50 and arrives in Gaborone at 06 35 the next morning. How long is the journey?

Show solution

Step 1 — 21 50 to midnight: 2 h 10 min.

Step 2 — midnight to 06 35: 6 h 35 min.

Step 3 — total: 2 h 10 min + 6 h 35 min = 8 h 45 min.

Why: split at midnight — never subtract clock times like ordinary decimals (06 35 − 21 50 makes no sense as arithmetic).

🚫 No calculator2 marks

Write 3.7 hours in hours and minutes.

Show solution

\(0.7\times60 = 42\), so 3.7 h = 3 h 42 min.

Why: the decimal part is a fraction of 60 minutes — 3 h 70 min is the trap answer.

4 Common mistakes
  • Treating 2.5 hours as 2 h 50 min — decimals of an hour are converted by × 60.
  • Area/volume conversions using the length factor: 1 m² ≠ 100 cm².
  • Subtracting times as if they were decimal numbers instead of counting through the hour.
  • Missing “the next day” in overnight journeys.
5 In the exam
  • Timetable reading is a Paper 1/2 classic — worth easy marks if you count time carefully.
  • Unit conversion is rarely a question on its own; it hides inside area, volume, density and speed questions — a wrong conversion poisons all the marks after it.
6 Stretch & challenge
⭐ Challenge 1🔢 Calculator5 marks

A night bus leaves Kasane at 21 40 and arrives in Gaborone at 07 15 the next morning. (a) How long is the journey? (b) The bus stopped for a total of 45 minutes on the way. The route is 940 km. Find the bus’s average speed while it was moving, to 3 significant figures.

Show full solution

(a) Step 1 — 21 40 to midnight: 2 h 20 min.

Step 2 — midnight to 07 15: 7 h 15 min.

Step 3 — total: 2 h 20 + 7 h 15 = 9 h 35 min.

(b) Step 1 — moving time \(= 9\,\text{h}\,35-45\,\text{min} = 8\,\text{h}\,50\,\text{min}\).

Step 2 — in hours: \(8\,\text{h}\,50 = 8\dfrac{50}{60} = 8.8333\ldots\) h.

Step 3 — speed \(= \dfrac{940}{8.8333\ldots} = 106.41\ldots = \mathbf{106\ km/h}\).

Why this works: split overnight times at midnight; convert minutes to a fraction of an hour BEFORE dividing; and keep the unrounded 8.8333… in the calculator.
⭐ Challenge 2🚫 No calculator4 marks

A tap drips 250 ml of water every 4 minutes. How many litres does it waste in a full day?

Show full solution

Step 1 — per minute: \(\dfrac{250}{4} = 62.5\) ml.

Step 2 — minutes in a day: \(24\times60 = 1\,440\).

Step 3 — per day: \(62.5\times1440 = 90\,000\) ml.

Step 4 — convert: \(\dfrac{90\,000}{1\,000} = \mathbf{90}\) litres.

Why this works: chain the units one step at a time (ml per min → min per day → ml per day → litres). Alternative route: \(1440\div4 = 360\) four-minute blocks, \(360\times250 = 90\,000\) ml — same answer, good self-check.
7 Exercise — in your book

📓 Write your answers in your exercise book. No peeking — reveal the answers only when finished, and mark your own work. Levels: 🟢 warm-up · 🔵 exam level · 🟠 stretch.

  1. 🟢 Convert 5.2 km to metres.
  2. 🟢 Convert 3 500 g to kg.
  3. 🟢 Convert 2.5 litres to ml.
  4. 🟢 Write 4.25 hours in hours and minutes.
  5. 🔵 Convert 0.8 m² to cm².
  6. 🔵 A film starts at 14 45 and lasts 3 h 50 min. When does it end?
  7. 🔵 How long is it from 09 12 to 13 05?
  8. 🟠 Convert 7 200 000 cm³ to m³.
Show answers — mark your work
  1. 5 200 m
  2. 3.5 kg
  3. 2 500 ml
  4. 4 h 15 min
  5. \(0.8\times10\,000 = 8\,000\) cm²
  6. 18 35
  7. 3 h 53 min
  8. \(\div1\,000\,000 = 7.2\) m³
Marking guide: 7–8 correct — excellent, move on. 5–6 — redo the ones you missed. Below 5 — work through the lesson again, then retry this exercise. Every question you fix yourself is a mark gained in the real exam.
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