Year 11 Maths: Convert rates and measurements: metric units

Understanding Metric Units

Metric units are a standard way of measuring things. They are used around the world and make it easier to understand and compare measurements. The metric system includes units for length, mass, and volume, among others. Here, we will explore how to convert between different metric units.

Key Metric Units

1. Length:
   • Millimetres (mm)
   • Centimetres (cm)
   • Metres (m)
   • Kilometres (km)
2. Mass:
   • Milligrams (mg)
   • Grams (g)
   • Kilograms (kg)
3. Volume:
   • Millilitres (ml)
   • Litres (l)

Conversion Basics

To convert between metric units, you can use the following key rules:

1. Length:
   • 1 cm = 10 mm
   • 1 m = 100 cm
   • 1 km = 1000 m
2. Mass:
   • 1 g = 1000 mg
   • 1 kg = 1000 g
3. Volume:
   • 1 l = 1000 ml

Tips for Conversion

• Moving Up: When you convert to a larger unit (like from grams to kilograms), you divide.
• Moving Down: When you convert to a smaller unit (like from kilograms to grams), you multiply.

Example 1: Length Conversion

Convert 5 metres to centimetres.

• Since 1 m = 100 cm, you multiply: $$5 \text{ m} \times 100 = 500 \text{ cm}$$

Example 2: Mass Conversion

Convert 2500 grams to kilograms.

• Since 1 kg = 1000 g, you divide: $$2500 \text{ g} \div 1000 = 2.5 \text{ kg}$$

Practice Questions

Easy Level Questions

1. Convert 1500 millilitres to litres.
2. How many grams are in 2.5 kg?
3. Convert 300 cm to metres.
4. Convert 5000 mg to grams.
5. Convert 1 km to metres.
6. How many millimetres are in 4 cm?
7. Convert 2.2 kg to grams.
8. Convert 750 ml to litres.
9. How many grams are in 500 mg?
10. Convert 3 m to cm.
11. How many millimetres are in 1.5 cm?
12. Convert 250 ml to litres.
13. Convert 700 g to kg.
14. How many grams are in 8000 mg?
15. Convert 4 km to metres.
16. How many centimetres are in 5 m?
17. Convert 1.5 kg to grams.
18. Convert 50 ml to litres.
19. How many millilitres are in 1.2 l?
20. Convert 600 mg to grams.

Medium Level Questions

1. Convert 8.5 m to cm.
2. Convert 3.5 kg to grams.
3. How many litres are in 2500 ml?
4. Convert 5 km to m.
5. Convert 1200 mg to g.
6. How many cm are in 2.5 m?
7. Convert 350 ml to litres.
8. If 1 l = 1000 ml, how many ml are in 3 l?
9. Convert 200 g to kg.
10. Convert 1.25 km to m.
11. How many grams are in 4500 mg?
12. Convert 600 ml to litres.
13. Convert 1.8 kg to grams.
14. How many cm are in 10 mm?
15. Convert 7500 g to kg.
16. Convert 0.5 l to ml.
17. Convert 400 m to km.
18. How many millilitres are in 0.75 l?
19. Convert 1000 mg to grams.
20. Convert 2.2 m to cm.

Hard Level Questions

1. Convert 2.5 km to m and then to cm.
2. How many grams are in 3.2 kg?
3. Convert 0.0025 kg to grams.
4. Convert 1500 ml to litres and then to gallons (1 l ≈ 0.219969 g).
5. Convert 0.3 l to ml and then to cl (centilitres).
6. How many millimetres are in 4.5 m?
7. Convert 600 g to kg and then to mg.
8. If 1 kg = 1000 g, how many grams are in 5 kg?
9. Convert 75 cm to m and then to mm.
10. Convert 1.75 l to ml and then to cl.
11. If 1.5 kg = x g, find x.
12. Convert 2.3 m to cm and then to mm.
13. How many ml are there in 4.2 l?
14. Convert 0.75 kg to g and then to mg.
15. Convert 1250 ml to l and then to cl.
16. How many grams are in 0.004 kg?
17. Convert 2.2 m to cm and then to mm.
18. If 3.5 kg = x mg, find x.
19. Convert 0.1 l to ml and then to cl.
20. Convert 0.005 kg to g.

Answers

Easy Level Answers

1. 1.5 l
2. 2500 g
3. 3 m
4. 5 g
5. 1000 m
6. 40 mm
7. 2200 g
8. 0.75 l
9. 0.5 g
10. 300 cm
11. 15 mm
12. 0.25 l
13. 0.7 kg
14. 8 g
15. 4000 m
16. 500 cm
17. 1500 g
18. 0.05 l
19. 1200 ml
20. 0.6 g

Medium Level Answers

1. 850 cm
2. 3500 g
3. 2.5 l
4. 5000 m
5. 1.2 g
6. 250 cm
7. 0.35 l
8. 3000 ml
9. 0.2 kg
10. 1250 m
11. 4.5 g
12. 0.6 l
13. 1800 g
14. 10 cm
15. 7.5 kg
16. 500 ml
17. 400 m
18. 750 ml
19. 1000 g
20. 220 cm

Hard Level Answers

1. 2500 m and 250000 cm
2. 3200 g
3. 2500 g
4. 1.5 g
5. 30 cl
6. 4500 mm
7. 600000 mg
8. 5000 g
9. 750 mm
10. 1750 ml and 175 cl
11. 1500 g
12. 230 cm and 2300 mm
13. 4200 ml
14. 750 g and 750000 mg
15. 1.25 l and 125 cl
16. 5 g
17. 220 cm and 2200 mm
18. 3500 mg
19. 100 ml and 10 cl
20. 5 g

Feel free to practice these conversions and refer back to the key rules to help you along the way!