Metric Conversions worksheet with tables and word problems for learning unit conversions.

Problem Analysis:

The image contains a worksheet on metric conversions. The tasks involve converting measurements between different metric units (e.g., millimeters to centimeters, grams to kilograms) and solving word problems related to these conversions. Below is a detailed breakdown and solution for each section.

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Section A: Metric Conversions (Millimeters, Centimeters, Meters, Kilometers)

#### Task:
For each measurement, find its equivalent in millimeters (mm), centimeters (cm), meters (m), or kilometers (km).

#### Solution:

1. 30 mm:
- 30 mm = 3 cm (since 1 cm = 10 mm)
- 30 mm = 0.03 m (since 1 m = 1000 mm)
- 30 mm = 0.00003 km (since 1 km = 1,000,000 mm)

2. 80 cm:
- 80 cm = 800 mm (since 1 cm = 10 mm)
- 80 cm = 0.8 m (since 1 m = 100 cm)
- 80 cm = 0.0008 km (since 1 km = 100,000 cm)

3. 250 m:
- 250 m = 250,000 mm (since 1 m = 1000 mm)
- 250 m = 25,000 cm (since 1 m = 100 cm)
- 250 m = 0.25 km (since 1 km = 1000 m)

4. 4000 m:
- 4000 m = 4,000,000 mm (since 1 m = 1000 mm)
- 4000 m = 400,000 cm (since 1 m = 100 cm)
- 4000 m = 4 km (since 1 km = 1000 m)

5. 7 cm:
- 7 cm = 70 mm (since 1 cm = 10 mm)
- 7 cm = 0.07 m (since 1 m = 100 cm)
- 7 cm = 0.00007 km (since 1 km = 100,000 cm)

6. 9.4 m:
- 9.4 m = 9400 mm (since 1 m = 1000 mm)
- 9.4 m = 940 cm (since 1 m = 100 cm)
- 9.4 m = 0.0094 km (since 1 km = 1000 m)

7. 13.8 km:
- 13.8 km = 13,800,000 mm (since 1 km = 1,000,000 mm)
- 13.8 km = 1,380,000 cm (since 1 km = 100,000 cm)
- 13.8 km = 13,800 m (since 1 km = 1000 m)

---

Section B: Kilograms and Grams

#### Task:
For each measurement, find its equivalent in kg or g.

#### Solution:

1. 5000 g:
- 5000 g = 5 kg (since 1 kg = 1000 g)

2. 10000 g:
- 10000 g = 10 kg (since 1 kg = 1000 g)

3. 125 g:
- 125 g = 0.125 kg (since 1 kg = 1000 g)

4. 3010 g:
- 3010 g = 3.01 kg (since 1 kg = 1000 g)

5. 73 g:
- 73 g = 0.073 kg (since 1 kg = 1000 g)

6. 6.65 kg:
- 6.65 kg = 6650 g (since 1 kg = 1000 g)

7. 170 g:
- 170 g = 0.17 kg (since 1 kg = 1000 g)

8. 50 kg:
- 50 kg = 50,000 g (since 1 kg = 1000 g)

9. 21.4 kg:
- 21.4 kg = 21,400 g (since 1 kg = 1000 g)

10. 0.371 kg:
- 0.371 kg = 371 g (since 1 kg = 1000 g)

---

Section C: Complete the Table by Solving Each Conversion

#### Task:
Complete the table by converting the given measurements.

#### Solution:

1. 8000 m:
- 8000 m = 8 km (since 1 km = 1000 m)
- 8000 m = 800,000 cm (since 1 m = 100 cm)

2. 7330 mm:
- 7330 mm = 7.33 m (since 1 m = 1000 mm)
- 7330 mm = 733 cm (since 1 cm = 10 mm)

3. 600 cm:
- 600 cm = 6 m (since 1 m = 100 cm)
- 600 cm = 0.006 km (since 1 km = 100,000 cm)

4. 6 m:
- 6 m = 600 cm (since 1 m = 100 cm)
- 6 m = 0.006 km (since 1 km = 1000 m)

5. 14.4 m:
- 14.4 m = 1440 cm (since 1 m = 100 cm)
- 14.4 m = 0.0144 km (since 1 km = 1000 m)

6. 0.07 m:
- 0.07 m = 7 cm (since 1 m = 100 cm)
- 0.07 m = 0.00007 km (since 1 km = 1000 m)

7. 5 km:
- 5 km = 5000 m (since 1 km = 1000 m)
- 5 km = 500,000 cm (since 1 km = 100,000 cm)

8. 17.1 km:
- 17.1 km = 17,100 m (since 1 km = 1000 m)
- 17.1 km = 1,710,000 cm (since 1 km = 100,000 cm)

9. 0.0058 km:
- 0.0058 km = 5.8 m (since 1 km = 1000 m)
- 0.0058 km = 580 cm (since 1 km = 100,000 cm)

---

Section D: Word Problems

#### Problem 1:
A 200-keeper weighs three baby koalas at 0.5 kg, 0.619 kg, 7.09 g. Work out the total weight of the three koalas:
a. In kilograms
b. In grams

##### Solution:
1. Convert all weights to kilograms:
- First koala: 0.5 kg
- Second koala: 0.619 kg
- Third koala: 7.09 g = 0.00709 kg (since 1 kg = 1000 g)

2. Add the weights:
\[
0.5 + 0.619 + 0.00709 = 1.12609 \text{ kg}
\]

3. Convert the total weight to grams:
\[
1.12609 \text{ kg} = 1126.09 \text{ g} \quad (\text{since } 1 \text{ kg} = 1000 \text{ g})
\]

##### Final Answers:
a. 1.12609 kg
b. 1126.09 g

---

#### Problem 2:
An athlete runs 8.5 laps around a race track. If a race track measures 400 m, work out the total distance run by the athlete:
a. In kilometers
b. In centimeters

##### Solution:
1. Calculate the total distance in meters:
\[
8.5 \text{ laps} \times 400 \text{ m/lap} = 3400 \text{ m}
\]

2. Convert meters to kilometers:
\[
3400 \text{ m} = 3.4 \text{ km} \quad (\text{since } 1 \text{ km} = 1000 \text{ m})
\]

3. Convert meters to centimeters:
\[
3400 \text{ m} = 340,000 \text{ cm} \quad (\text{since } 1 \text{ m} = 100 \text{ cm})
\]

##### Final Answers:
a. 3.4 km
b. 340,000 cm

---

Final Answer Summary:

\[
\boxed{
\begin{aligned}
&\text{Section A:} \\
&1. 30 \text{ mm} = 3 \text{ cm}, 0.03 \text{ m}, 0.00003 \text{ km} \\
&2. 80 \text{ cm} = 800 \text{ mm}, 0.8 \text{ m}, 0.0008 \text{ km} \\
&3. 250 \text{ m} = 250,000 \text{ mm}, 25,000 \text{ cm}, 0.25 \text{ km} \\
&4. 4000 \text{ m} = 4,000,000 \text{ mm}, 400,000 \text{ cm}, 4 \text{ km} \\
&5. 7 \text{ cm} = 70 \text{ mm}, 0.07 \text{ m}, 0.00007 \text{ km} \\
&6. 9.4 \text{ m} = 9400 \text{ mm}, 940 \text{ cm}, 0.0094 \text{ km} \\
&7. 13.8 \text{ km} = 13,800,000 \text{ mm}, 1,380,000 \text{ cm}, 13,800 \text{ m} \\
\\
&\text{Section B:} \\
&1. 5000 \text{ g} = 5 \text{ kg} \\
&2. 10000 \text{ g} = 10 \text{ kg} \\
&3. 125 \text{ g} = 0.125 \text{ kg} \\
&4. 3010 \text{ g} = 3.01 \text{ kg} \\
&5. 73 \text{ g} = 0.073 \text{ kg} \\
&6. 6.65 \text{ kg} = 6650 \text{ g} \\
&7. 170 \text{ g} = 0.17 \text{ kg} \\
&8. 50 \text{ kg} = 50,000 \text{ g} \\
&9. 21.4 \text{ kg} = 21,400 \text{ g} \\
&10. 0.371 \text{ kg} = 371 \text{ g} \\
\\
&\text{Section C:} \\
&1. 8000 \text{ m} = 8 \text{ km}, 800,000 \text{ cm} \\
&2. 7330 \text{ mm} = 7.33 \text{ m}, 733 \text{ cm} \\
&3. 600 \text{ cm} = 6 \text{ m}, 0.006 \text{ km} \\
&4. 6 \text{ m} = 600 \text{ cm}, 0.006 \text{ km} \\
&5. 14.4 \text{ m} = 1440 \text{ cm}, 0.0144 \text{ km} \\
&6. 0.07 \text{ m} = 7 \text{ cm}, 0.00007 \text{ km} \\
&7. 5 \text{ km} = 5000 \text{ m}, 500,000 \text{ cm} \\
&8. 17.1 \text{ km} = 17,100 \text{ m}, 1,710,000 \text{ cm} \\
&9. 0.0058 \text{ km} = 5.8 \text{ m}, 580 \text{ cm} \\
\\
&\text{Section D:} \\
&1. \text{Total weight of koalas:} \\
&a. 1.12609 \text{ kg} \\
&b. 1126.09 \text{ g} \\
&2. \text{Distance run by athlete:} \\
&a. 3.4 \text{ km} \\
&b. 340,000 \text{ cm}
\end{aligned}
}
\]