Comprehensive metric conversions worksheet featuring tables for length and mass, plus challenging word problems.

Let's solve each section of the Metric Conversions worksheet step by step and explain the solutions clearly.

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🔷 Section A: Length Conversions (mm, cm, m, km)

We need to convert between millimetres (mm), centimetres (cm), metres (m), and kilometres (km).
Remember:
- 10 mm = 1 cm
- 100 cm = 1 m
- 1000 m = 1 km

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#### Table 1: Millimetres ↔ Centimetres
| Millimetres | Centimetres |
|-------------|-------------|
| 30 mm | 3 cm | → $ 30 \div 10 = 3 $ |
| 80 mm | 8 cm | → $ 80 \div 10 = 8 $ |
| 200 mm | 20 cm | → $ 200 \div 10 = 20 $ |
| 70 mm | 7 cm | → $ 7 \times 10 = 70 $ |
| 94 mm | 9.4 cm | → $ 9.4 \times 10 = 94 $ |
| 138 mm | 13.8 cm | → $ 13.8 \times 10 = 138 $ |

> ✔ Fill in missing values:
> - 7 cm = 70 mm
> - 9.4 cm = 94 mm
> - 13.8 cm = 138 mm

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#### Table 2: Centimetres ↔ Metres
| Centimetres | Metres |
|-------------|--------|
| 200 cm | 2 m | → $ 200 \div 100 = 2 $ |
| 420 cm | 4.2 m | → $ 420 \div 100 = 4.2 $ |
| 85 cm | 0.85 m | → $ 85 \div 100 = 0.85 $ |
| 400 cm | 4 m | → $ 4 \times 100 = 400 $ |
| 890 cm | 8.9 m | → $ 8.9 \times 100 = 890 $ |
| 50 cm | 0.5 m | → $ 0.5 \times 100 = 50 $ |

> ✔ Fill in missing values:
> - 4 m = 400 cm
> - 8.9 m = 890 cm
> - 0.5 m = 50 cm

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#### Table 3: Metres ↔ Kilometres
| Metres | Kilometres |
|----------|------------|
| 4000 m | 4 km | → $ 4000 \div 1000 = 4 $ |
| 5800 m | 5.8 km | → $ 5800 \div 1000 = 5.8 $ |
| 900 m | 0.9 km | → $ 900 \div 1000 = 0.9 $ |
| 7000 m | 7 km | → $ 7 \times 1000 = 7000 $ |
| 8300 m | 8.3 km | → $ 8.3 \times 1000 = 8300 $ |
| 15000 m | 15 km | → $ 15 \times 1000 = 15000 $ |

> ✔ Fill in missing values:
> - 7 km = 7000 m
> - 8.3 km = 8300 m
> - 15 km = 15000 m

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🔷 Section B: Mass Conversions (g ↔ kg)

We know:
- 1000 g = 1 kg

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#### Left Table: Grams → Kilograms
| Grams | Kilograms |
|----------|-----------|
| 5000 g | 5 kg | → $ 5000 \div 1000 = 5 $ |
| 10000 g | 10 kg | → $ 10000 \div 1000 = 10 $ |
| 1220 g | 1.22 kg | → $ 1220 \div 1000 = 1.22 $ |
| 3010 g | 3.01 kg | → $ 3010 \div 1000 = 3.01 $ |
| 738 g | 0.738 kg | → $ 738 \div 1000 = 0.738 $ |

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#### Right Table: Kilograms → Grams
| Grams | Kilograms |
|-----------|-----------|
| 6050 g | 6.05 kg | → $ 6.05 \times 1000 = 6050 $ |
| 170000 g | 170 kg | → $ 170 \times 1000 = 170000 $ |
| 50000 g | 50 kg | → $ 50 \times 1000 = 50000 $ |
| 21400 g | 21.4 kg | → $ 21.4 \times 1000 = 21400 $ |
| 371 g | 0.371 kg | → $ 0.371 \times 1000 = 371 $ |

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🔷 Section C: Complete the table so each row is equal

We need to convert between units using standard conversion factors.

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#### Left Table: Millimetres ↔ Metres
| Millimetres | Metres |
|-------------|--------|
| 8000 mm | 8 m | → $ 8000 \div 1000 = 8 $ |
| 73300 mm | 73.3 m | → $ 73300 \div 1000 = 73.3 $ |
| 600 mm | 0.6 m | → $ 600 \div 1000 = 0.6 $ |
| 6000 mm | 6 m | → $ 6 \times 1000 = 6000 $ |
| 14400 mm | 14.4 m | → $ 14.4 \times 1000 = 14400 $ |
| 70 mm | 0.07 m | → $ 0.07 \times 1000 = 70 $ |

> ✔ Fill in:
> - 6 m = 6000 mm
> - 14.4 m = 14400 mm
> - 0.07 m = 70 mm

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#### Right Table: Centimetres ↔ Kilometres
| Centimetres | Kilometres |
|-------------|------------|
| 100000 cm | 1 km | → $ 100000 \div 100000 = 1 $ |
| 42000 cm | 0.42 km | → $ 42000 \div 100000 = 0.42 $ |
| 340 cm | 0.0034 km | → $ 340 \div 100000 = 0.0034 $ |
| 500000 cm | 5 km | → $ 5 \times 100000 = 500000 $ |
| 1710000 cm | 17.1 km | → $ 17.1 \times 100000 = 1710000 $ |
| 5800 cm | 0.0058 km | → $ 0.0058 \times 100000 = 5800 $ |

> ✔ Fill in:
> - 5 km = 500000 cm
> - 17.1 km = 1710000 cm
> - 0.0058 km = 5800 cm

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🔷 Section D: Word Problems

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#### 1) Total weight of three baby koalas:
Weights:
- 0.5 kg
- 0.616 kg
- 706 g

First, convert all to kilograms:

- 706 g = $ 706 \div 1000 = 0.706 $ kg

Now add:
$$
0.5 + 0.616 + 0.706 = 1.822 \text{ kg}
$$

✔ a) Total weight in kilograms: 1.822 kg

Now convert to grams:
$$
1.822 \text{ kg} = 1.822 \times 1000 = 1822 \text{ g}
$$

✔ b) Total weight in grams: 1822 g

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#### 2) Distance run by athlete:
- 8.5 laps around a 400 m track

Total distance:
$$
8.5 \times 400 = 3400 \text{ m}
$$

Now convert:

✔ a) In kilometres:
$$
3400 \div 1000 = 3.4 \text{ km}
$$

✔ b) In centimetres:
$$
3400 \text{ m} = 3400 \times 100 = 340000 \text{ cm}
$$

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✔ Final Answers Summary

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#### Section A

Millimetres ↔ Centimetres
| mm | cm |
|------|-----|
| 30 | 3 |
| 80 | 8 |
| 200 | 20 |
| 70 | 7 |
| 94 | 9.4 |
| 138 | 13.8|

Centimetres ↔ Metres
| cm | m |
|------|------|
| 200 | 2 |
| 420 | 4.2 |
| 85 | 0.85 |
| 400 | 4 |
| 890 | 8.9 |
| 50 | 0.5 |

Metres ↔ Kilometres
| m | km |
|-------|------|
| 4000 | 4 |
| 5800 | 5.8 |
| 900 | 0.9 |
| 7000 | 7 |
| 8300 | 8.3 |
| 15000 | 15 |

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#### Section B

Grams ↔ Kilograms
| g | kg |
|-------|-------|
| 5000 | 5 |
| 10000 | 10 |
| 1220 | 1.22 |
| 3010 | 3.01 |
| 738 | 0.738 |

| g | kg |
|--------|--------|
| 6050 | 6.05 |
| 170000 | 170 |
| 50000 | 50 |
| 21400 | 21.4 |
| 371 | 0.371 |

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#### Section C

Millimetres ↔ Metres
| mm | m |
|--------|-------|
| 8000 | 8 |
| 73300 | 73.3 |
| 600 | 0.6 |
| 6000 | 6 |
| 14400 | 14.4 |
| 70 | 0.07 |

Centimetres ↔ Kilometres
| cm | km |
|----------|--------|
| 100000 | 1 |
| 42000 | 0.42 |
| 340 | 0.0034 |
| 500000 | 5 |
| 1710000 | 17.1 |
| 5800 | 0.0058 |

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#### Section D

1) Total weight of koalas:
- a) 1.822 kg
- b) 1822 g

2) Distance run:
- a) 3.4 km
- b) 340000 cm

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✔ All problems solved! Let me know if you'd like this formatted as a printable PDF or want explanations for any specific part.