Units of Measurement
Before you can measure perimeter, area, or any quantity, you need to know the units of measurement. A measurement without a unit is meaningless — saying "the table is 120" tells you nothing, but "the table is 120 cm" tells you exactly how long it is.
In India (and most of the world), we use the metric system — metres for length, grams for weight, and litres for capacity. In this topic, you will learn the standard units for length, area, weight, and capacity, and how to convert between them.
Understanding units and conversions is essential for solving mensuration problems (perimeter, area) correctly.
What is Units of Measurement?
Definition: A unit of measurement is a standard quantity used to express a physical measurement.
Units of Length:
- 1 kilometre (km) = 1,000 metres (m)
- 1 metre (m) = 100 centimetres (cm)
- 1 centimetre (cm) = 10 millimetres (mm)
- 1 m = 1,000 mm
- 1 km = 1,00,000 cm = 10,00,000 mm
Units of Area:
- 1 m² = 10,000 cm² (because 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm²)
- 1 km² = 10,00,000 m² (1 km = 1000 m, so 1 km² = 1000 × 1000)
- 1 hectare = 10,000 m² (used for measuring land)
- 1 km² = 100 hectares
Units of Weight (Mass):
- 1 kilogram (kg) = 1,000 grams (g)
- 1 gram (g) = 1,000 milligrams (mg)
- 1 quintal = 100 kg
- 1 tonne = 1,000 kg
Units of Capacity (Volume):
- 1 litre (L) = 1,000 millilitres (mL)
- 1 kilolitre (kL) = 1,000 litres
Types and Properties
1. Converting Larger to Smaller Units
Multiply by the conversion factor.
- 3 km = 3 × 1000 = 3,000 m.
- 2.5 m = 2.5 × 100 = 250 cm.
- 4 kg = 4 × 1000 = 4,000 g.
2. Converting Smaller to Larger Units
Divide by the conversion factor.
- 5,000 m = 5,000 ÷ 1000 = 5 km.
- 350 cm = 350 ÷ 100 = 3.5 m.
- 2,500 g = 2,500 ÷ 1000 = 2.5 kg.
3. Area Unit Conversions
Since area is 2-dimensional, the conversion factor is squared.
- 1 m² = (100 cm)² = 10,000 cm².
- 3 m² = 3 × 10,000 = 30,000 cm².
- 50,000 cm² = 50,000 ÷ 10,000 = 5 m².
4. Mixed Units
- 2 m 35 cm = 2.35 m = 235 cm.
- 5 kg 200 g = 5.2 kg = 5,200 g.
Solved Examples
Example 1: Example 1: km to m
Problem: Convert 3.5 km to metres.
Solution:
- 1 km = 1,000 m.
- 3.5 km = 3.5 × 1,000 = 3,500 m.
Answer: 3,500 m
Example 2: Example 2: cm to m
Problem: Convert 425 cm to metres.
Solution:
- 1 m = 100 cm.
- 425 cm = 425 ÷ 100 = 4.25 m.
Answer: 4.25 m
Example 3: Example 3: g to kg
Problem: Convert 3,750 g to kg.
Solution:
- 1 kg = 1,000 g.
- 3,750 g = 3,750 ÷ 1,000 = 3.75 kg.
Answer: 3.75 kg
Example 4: Example 4: mL to litres
Problem: Convert 2,500 mL to litres.
Solution:
- 1 litre = 1,000 mL.
- 2,500 mL = 2,500 ÷ 1,000 = 2.5 litres.
Answer: 2.5 litres
Example 5: Example 5: Area conversion (m² to cm²)
Problem: Convert 2 m² to cm².
Solution:
- 1 m² = 10,000 cm².
- 2 m² = 2 × 10,000 = 20,000 cm².
Answer: 20,000 cm²
Example 6: Example 6: cm² to m²
Problem: Convert 50,000 cm² to m².
Solution:
- 50,000 ÷ 10,000 = 5 m².
Answer: 5 m²
Example 7: Example 7: Mixed units
Problem: Express 3 m 45 cm in cm and in m.
Solution:
- In cm: 3 m = 300 cm. So 3 m 45 cm = 300 + 45 = 345 cm.
- In m: 45 cm = 0.45 m. So 3 m 45 cm = 3.45 m.
Answer: 345 cm or 3.45 m.
Example 8: Example 8: Adding with different units
Problem: Add: 2 km 300 m + 1 km 750 m.
Solution:
- 2 km 300 m = 2,300 m. 1 km 750 m = 1,750 m.
- Total = 2,300 + 1,750 = 4,050 m = 4 km 50 m.
Answer: 4 km 50 m
Example 9: Example 9: Hectare conversion
Problem: A farm is 3 hectares. Express in m².
Solution:
- 1 hectare = 10,000 m².
- 3 hectares = 3 × 10,000 = 30,000 m².
Answer: 30,000 m²
Example 10: Example 10: Weight in mixed units
Problem: Express 7 kg 250 g in kg (as a decimal) and in grams.
Solution:
- In grams: 7 kg = 7,000 g. Total = 7,000 + 250 = 7,250 g.
- In kg: 250 g = 0.25 kg. Total = 7.25 kg.
Answer: 7,250 g or 7.25 kg.
Real-World Applications
Construction: Builders measure rooms in metres (length), tiles in cm², and land in hectares or m². Correct unit conversion avoids costly mistakes.
Shopping: Groceries are sold in kg and g. Milk and oil in litres and mL. Understanding units helps you compare prices and quantities.
Travel: Distances are in km. Car odometers show km. Flight altitudes are in metres or feet. Unit awareness helps with travel planning.
Cooking: Recipes use grams, litres, and millilitres. Converting between cups and mL, or between kg and g, is essential for following recipes.
Science: All scientific measurements require correct units. Mixing up mm and cm, or g and kg, can cause experiment failures.
Key Points to Remember
- Length: 1 km = 1,000 m. 1 m = 100 cm. 1 cm = 10 mm.
- Area: 1 m² = 10,000 cm². 1 hectare = 10,000 m². 1 km² = 100 hectares.
- Weight: 1 kg = 1,000 g. 1 g = 1,000 mg. 1 tonne = 1,000 kg.
- Capacity: 1 litre = 1,000 mL. 1 kL = 1,000 litres.
- Larger to smaller: multiply. Smaller to larger: divide.
- For area conversions, square the conversion factor (1 m = 100 cm → 1 m² = 10,000 cm²).
- Always check that units match before adding or subtracting measurements.
- A measurement without a unit is meaningless.
Practice Problems
- Convert: (a) 4.2 km to m, (b) 560 cm to m, (c) 8,500 g to kg.
- Convert: (a) 3 m² to cm², (b) 75,000 cm² to m².
- Add: 5 km 400 m + 3 km 850 m. Express in km and m.
- A table is 1 m 75 cm long. Express in cm and in metres.
- Convert 2.5 hectares to m².
- A juice bottle has 1.5 litres. Express in mL.
- Subtract: 5 kg 200 g − 2 kg 750 g.
- A rectangular garden is 50 m × 30 m. Find its area in m² and hectares.
Frequently Asked Questions
Q1. What is the metric system?
The metric system is a decimal system of measurement based on multiples of 10. It uses metres for length, grams for weight, and litres for capacity. It is used in India and most countries worldwide.
Q2. How do I convert from a larger unit to a smaller unit?
Multiply. For example, 3 km to metres: 3 × 1000 = 3000 m. Going to a smaller unit means you need more of them, so the number gets bigger.
Q3. How do I convert from a smaller unit to a larger unit?
Divide. For example, 500 cm to metres: 500 ÷ 100 = 5 m. Going to a larger unit means you need fewer of them, so the number gets smaller.
Q4. Why is 1 m² equal to 10,000 cm² and not 100 cm²?
Because area is 2-dimensional. 1 m = 100 cm, so 1 m² = 100 cm × 100 cm = 10,000 cm². You square the conversion factor.
Q5. What is a hectare?
A hectare is a unit of area equal to 10,000 m² (100 m × 100 m). It is used to measure large areas like farms and parks. 1 km² = 100 hectares.
Q6. What is the difference between weight and mass?
In everyday language, weight and mass are used interchangeably. Technically, mass is the amount of matter (measured in kg), and weight is the force of gravity on that mass. At Class 6 level, you can use them as the same.
Q7. Why do we need to convert units?
You cannot add 2 km + 500 m directly. You must convert to the same unit first: 2 km + 0.5 km = 2.5 km, or 2000 m + 500 m = 2500 m. Same unit = correct calculation.
Q8. Is 1 litre the same as 1 kg?
For water, yes — 1 litre of water weighs approximately 1 kg. But for other liquids (oil, milk), the weight per litre is different. Litre measures volume (capacity), and kg measures mass (weight).
