Understanding and mastering metric units and their conversions are fundamental skills in maths, necessary for solving a wide range of problems in both academic settings and everyday life. This section covers the basics of metric units for length, area, volume, and mass, along with key conversion techniques.
Introduction to Metric Units
The metric system is an international standard based on the number 10. It includes units for length (metres), mass (grams), and volume (litres).
Length Units
![Lengths Units](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F544ea69b-eec1-4898-8eb5-57eda8e1b8d1-file.png&w=1080&q=75)
Image courtesy of BYJUS
- Millimetre (mm)
- Centimetre (cm): 10 mm
- Metre (m): 100 cm
- Kilometre (km): 1,000 m
Area Units
![Area Units](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fa4641acb-b3ed-4d7e-8e20-45f25608aafe-file.png&w=1080&q=75)
Image courtesy of Math Space
- Square Millimetre mm2
- Square Centimetre cm2: 100 mm2
- Square Metre m2: 10,000 cm2
- Square Kilometre km2: 1,000,000 m2
Volume Units
![Volume Units](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F97be4686-22fd-4283-b029-549d79c0f3f6-file.png&w=1080&q=75)
Image courtesy of Math Space
- Cubic Millimetre mm3
- Cubic Centimetre cm3or Millilitre ml
- Cubic Metre m3:1,000,000 cm3
- Litre l: 1,000 ml
Mass Units
![Mass Units](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F0b33aa31-1327-4474-a752-7b97dc66dbac-file.png&w=1080&q=75)
Image courtesy of Cue Math
- Gram g
- Kilogram kg: 1,000 g
Converting Between Units
Conversion involves multiplying or dividing by 10, 100, or 1,000, depending on the relationship between the units.
Length Conversion Examples
Example 1: Convert 5,000 mm to metres.
- Solution: 5,000mm×1,000mm1m=5m
Example 2: Convert 7.5 km to metres.
- Solution: 7.5km×1km1,000m=7,500m
Area Conversion Examples
Example 3: Convert 2,000 cm2 to m2.
- Solution: 2,000cm2×10,000cm21m2=0.2m2
Volume Conversion Examples
Example 4: Convert 1,000,000 cm3 to m3.
- Solution: 1,000,000cm3×1,000,000cm31m3=1m3
Mass Conversion Example
Example 5: Convert 2,500 g to kilograms.
- Solution: 2,500g×1,000g1kg=2.5kg
Practice Problems
Problem 1: How many millilitres are in 3.5 litres?
Solution:
3.5l×1,000ml/l=3,500ml
Problem 2: Convert 9 km to millimetres.
Solution:
9km×1km1,000,000mm=9,000,000mm