Metric Conversions Worksheet | Printable Maths Worksheets - Free Printable

Solution to the Metric Conversions Worksheet

#### Section A: Kilometres, Metres, Centimetres, and Millimetres

The key conversions to remember:
- 1 km = 1000 m
- 1 m = 100 cm
- 1 cm = 10 mm

##### Table 1: Millimetres to Centimetres
1. 30 mm:
\( 30 \div 10 = 3 \) cm
Answer: 3 cm

2. 80 mm:
\( 80 \div 10 = 8 \) cm
Answer: 8 cm

3. 200 mm:
\( 200 \div 10 = 20 \) cm
Answer: 20 cm

4. 7 cm:
\( 7 \times 10 = 70 \) mm
Answer: 70 mm

5. 9.4 cm:
\( 9.4 \times 10 = 94 \) mm
Answer: 94 mm

6. 13.8 cm:
\( 13.8 \times 10 = 138 \) mm
Answer: 138 mm

##### Table 2: Centimetres to Metres
1. 200 cm:
\( 200 \div 100 = 2 \) m
Answer: 2 m

2. 420 cm:
\( 420 \div 100 = 4.2 \) m
Answer: 4.2 m

3. 85 cm:
\( 85 \div 100 = 0.85 \) m
Answer: 0.85 m

4. 4 m:
\( 4 \times 100 = 400 \) cm
Answer: 400 cm

5. 8.9 m:
\( 8.9 \times 100 = 890 \) cm
Answer: 890 cm

6. 0.5 m:
\( 0.5 \times 100 = 50 \) cm
Answer: 50 cm

##### Table 3: Metres to Kilometres
1. 4000 m:
\( 4000 \div 1000 = 4 \) km
Answer: 4 km

2. 5800 m:
\( 5800 \div 1000 = 5.8 \) km
Answer: 5.8 km

3. 900 m:
\( 900 \div 1000 = 0.9 \) km
Answer: 0.9 km

4. 7 km:
\( 7 \times 1000 = 7000 \) m
Answer: 7000 m

5. 8.3 km:
\( 8.3 \times 1000 = 8300 \) m
Answer: 8300 m

6. 15 km:
\( 15 \times 1000 = 15000 \) m
Answer: 15000 m

---

#### Section B: Kilograms and Grams

The key conversion to remember:
- 1 kg = 1000 g

##### Table 1: Grams to Kilograms
1. 5000 g:
\( 5000 \div 1000 = 5 \) kg
Answer: 5 kg

2. 10000 g:
\( 10000 \div 1000 = 10 \) kg
Answer: 10 kg

3. 1220 g:
\( 1220 \div 1000 = 1.22 \) kg
Answer: 1.22 kg

4. 3010 g:
\( 3010 \div 1000 = 3.01 \) kg
Answer: 3.01 kg

5. 738 g:
\( 738 \div 1000 = 0.738 \) kg
Answer: 0.738 kg

##### Table 2: Kilograms to Grams
1. 6.05 kg:
\( 6.05 \times 1000 = 6050 \) g
Answer: 6050 g

2. 170 kg:
\( 170 \times 1000 = 170000 \) g
Answer: 170000 g

3. 50 kg:
\( 50 \times 1000 = 50000 \) g
Answer: 50000 g

4. 21.4 kg:
\( 21.4 \times 1000 = 21400 \) g
Answer: 21400 g

5. 0.371 kg:
\( 0.371 \times 1000 = 371 \) g
Answer: 371 g

---

#### Section C: Complete the Table by Making Each Row Equal

##### Table 1: Millimetres to Metres
1. 8000 mm:
\( 8000 \div 1000 = 8 \) m
Answer: 8 m

2. 73300 mm:
\( 73300 \div 1000 = 73.3 \) m
Answer: 73.3 m

3. 600 mm:
\( 600 \div 1000 = 0.6 \) m
Answer: 0.6 m

4. 6 m:
\( 6 \times 1000 = 6000 \) mm
Answer: 6000 mm

5. 14.4 m:
\( 14.4 \times 1000 = 14400 \) mm
Answer: 14400 mm

6. 0.07 m:
\( 0.07 \times 1000 = 70 \) mm
Answer: 70 mm

##### Table 2: Centimetres to Kilometres
1. 100000 cm:
\( 100000 \div 100000 = 1 \) km
Answer: 1 km

2. 42000 cm:
\( 42000 \div 100000 = 0.42 \) km
Answer: 0.42 km

3. 340 cm:
\( 340 \div 100000 = 0.0034 \) km
Answer: 0.0034 km

4. 5 km:
\( 5 \times 100000 = 500000 \) cm
Answer: 500000 cm

5. 17.1 km:
\( 17.1 \times 100000 = 1710000 \) cm
Answer: 1710000 cm

6. 0.0058 km:
\( 0.0058 \times 100000 = 580 \) cm
Answer: 580 cm

---

#### Section D: Word Problems

##### Problem 1: Total Weight of Baby Koalas
The weights are given as:
- 0.5 kg
- 0.616 kg
- 706 g (convert to kg: \( 706 \div 1000 = 0.706 \) kg)

a. Total weight in kilograms:
Add the weights:
\[ 0.5 + 0.616 + 0.706 = 1.822 \text{ kg} \]
Answer: 1.822 kg

b. Total weight in grams:
Convert 1.822 kg to grams:
\[ 1.822 \times 1000 = 1822 \text{ g} \]
Answer: 1822 g

##### Problem 2: Distance Run by Athlete
The athlete runs 8.5 laps around a race track, and each lap is 400 m.

a. Total distance in kilometres:
First, calculate the total distance in metres:
\[ 8.5 \times 400 = 3400 \text{ m} \]
Convert to kilometres:
\[ 3400 \div 1000 = 3.4 \text{ km} \]
Answer: 3.4 km

b. Total distance in centimetres:
Convert 3400 m to centimetres:
\[ 3400 \times 100 = 340000 \text{ cm} \]
Answer: 340000 cm

---

Final Answers:

#### Section A
- Table 1: 3 cm, 8 cm, 20 cm, 70 mm, 94 mm, 138 mm
- Table 2: 2 m, 4.2 m, 0.85 m, 400 cm, 890 cm, 50 cm
- Table 3: 4 km, 5.8 km, 0.9 km, 7000 m, 8300 m, 15000 m

#### Section B
- Table 1: 5 kg, 10 kg, 1.22 kg, 3.01 kg, 0.738 kg
- Table 2: 6050 g, 170000 g, 50000 g, 21400 g, 371 g

#### Section C
- Table 1: 8 m, 73.3 m, 0.6 m, 6000 mm, 14400 mm, 70 mm
- Table 2: 1 km, 0.42 km, 0.0034 km, 500000 cm, 1710000 cm, 580 cm

#### Section D
- Problem 1:
- a. 1.822 kg
- b. 1822 g
- Problem 2:
- a. 3.4 km
- b. 340000 cm

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Section A: } \\
\text{Table 1: } 3 \text{ cm}, 8 \text{ cm}, 20 \text{ cm}, 70 \text{ mm}, 94 \text{ mm}, 138 \text{ mm} \\
\text{Table 2: } 2 \text{ m}, 4.2 \text{ m}, 0.85 \text{ m}, 400 \text{ cm}, 890 \text{ cm}, 50 \text{ cm} \\
\text{Table 3: } 4 \text{ km}, 5.8 \text{ km}, 0.9 \text{ km}, 7000 \text{ m}, 8300 \text{ m}, 15000 \text{ m} \\
\\
\text{Section B: } \\
\text{Table 1: } 5 \text{ kg}, 10 \text{ kg}, 1.22 \text{ kg}, 3.01 \text{ kg}, 0.738 \text{ kg} \\
\text{Table 2: } 6050 \text{ g}, 170000 \text{ g}, 50000 \text{ g}, 21400 \text{ g}, 371 \text{ g} \\
\\
\text{Section C: } \\
\text{Table 1: } 8 \text{ m}, 73.3 \text{ m}, 0.6 \text{ m}, 6000 \text{ mm}, 14400 \text{ mm}, 70 \text{ mm} \\
\text{Table 2: } 1 \text{ km}, 0.42 \text{ km}, 0.0034 \text{ km}, 500000 \text{ cm}, 1710000 \text{ cm}, 580 \text{ cm} \\
\\
\text{Section D: } \\
\text{Problem 1: } \\
\text{a. } 1.822 \text{ kg} \\
\text{b. } 1822 \text{ g} \\
\text{Problem 2: } \\
\text{a. } 3.4 \text{ km} \\
\text{b. } 340000 \text{ cm}
\end{array}
}
\]