MEASUREMENTS Notes, Quizzes & Revision

What are measurements?

Measurement is the process of finding the size, amount or degree of something using units. In Kenya (and most of the world) we use the metric system: metres (m), kilograms (kg), litres (L), seconds (s), degrees Celsius (°C), etc.

Common quantities and units

• Length / distance: millimetre (mm), centimetre (cm), metre (m), kilometre (km). Example: distance between Nairobi and Nakuru in km.
• Mass (weight): gram (g), kilogram (kg). Example: a bag of maize ≈ 90 kg (typical large sacks).
• Capacity / volume: millilitre (mL), litre (L). Example: jerrycans of water (20 L).
• Area: square metre (m²), hectare (ha = 10,000 m²). Example: farm plots measured in hectares.
• Time: seconds (s), minutes (min), hours (h), 24-hour clock used in transport schedules.
• Temperature: degrees Celsius (°C). Example: weather forecasts for Nairobi, Eldoret.

Tools used in Kenyan schools and at home

Ruler, tape measure, bathroom scales, kitchen scales, measuring jug (with mL markings), stopwatch, thermometer, measuring wheel, and GPS/road signs for kilometres.

Metric conversions — quick rules

Moving between metric units usually means multiplying or dividing by powers of 10. Use these steps:

• 1 km = 1 000 m. To go km → m, multiply by 1 000. To go m → km, divide by 1 000.
• 1 m = 100 cm; 1 cm = 10 mm.
• 1 kg = 1 000 g.
• 1 L = 1 000 mL. 1 m³ = 1 000 L (useful for water tanks).
• 1 ha = 10 000 m² (useful for farmland area).

Area and perimeter — formulas

• Rectangle: area = length × width (A = l × w). Units: m × m = m².
• Square: area = side².
• Triangle: area = 1/2 × base × height.
• Circle: area ≈ π × r² (π ≈ 3.14). Circumference = 2πr.
• Perimeter: sum of all sides (use m).

Volume and capacity — everyday uses

Volume is used for liquids and three-dimensional objects:

• Box (cuboid) volume = length × width × height (m³). To find litres, 1 m³ = 1 000 L.
• Water tank: calculate volume to know how many litres of water it holds.

Common conversions with worked examples

1. Convert 2.75 m to cm: 2.75 × 100 = 275 cm.
2. Convert 4 500 g to kg: 4 500 ÷ 1 000 = 4.5 kg.
3. Convert 0.6 km to m: 0.6 × 1 000 = 600 m.
4. Convert 2 500 m² to hectares: 2 500 ÷ 10 000 = 0.25 ha.

Practical classroom and home activities (brief)

Measure and record real things to practise:

• Length of classroom benches, gates, or the distance from school gate to the assembly point (use tape measure and record in m).
• Mass of produce (e.g., 1 kg of beans) using kitchen scales; compare with a 1 kg packet label.
• Measure water in a jerrycan (20 L) and calculate how many jerrycans fill a 500 L tank.

Tips for accuracy

• Read the measuring instrument at eye level.
• Start measurements from the zero mark on rulers and tapes.
• Use appropriate units (do not mix m and cm without converting).
• Repeat measurements and take the average if results differ slightly.

Practice questions

1. Convert 7.2 km to metres.
2. A maize sack weighs 90 kg. How many sacks equal 1 800 kg?
3. Find the area of a rectangular plot 50 m by 40 m (give answer in m² and ha).
4. A water tank is a cuboid: length 2 m, width 1.2 m, height 1.5 m. How many litres does it hold?
5. Convert 3 750 mL to litres.

Answers

1. 7.2 km = 7 200 m.
2. 1 800 ÷ 90 = 20 sacks.
3. Area = 50 × 40 = 2 000 m² = 0.20 ha (2 000 ÷ 10 000).
4. Volume = 2 × 1.2 × 1.5 = 3.6 m³ = 3 600 L.
5. 3 750 mL = 3.75 L.