Metric Conversions worksheet - Free Printable

Problem Explanation and Solution

The worksheet involves converting metric units of length, comparing lengths, and identifying the largest amount in each group. Let's solve it step by step.

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#### Part 1: Convert the following metric units of length

The metric system uses the following conversions:
- 1 km = 1000 m
- 1 m = 100 cm
- 1 cm = 10 mm

Using these relationships, we can solve each problem:

1. 5 km = ____ m
- \( 5 \text{ km} \times 1000 = 5000 \text{ m} \)
- Answer: 5000 m

2. 600 cm = ____ m
- \( 600 \text{ cm} \div 100 = 6 \text{ m} \)
- Answer: 6 m

3. 8 cm = ____ mm
- \( 8 \text{ cm} \times 10 = 80 \text{ mm} \)
- Answer: 80 mm

4. ____ km = 4000 m
- \( 4000 \text{ m} \div 1000 = 4 \text{ km} \)
- Answer: 4 km

5. ____ m = 900 cm
- \( 900 \text{ cm} \div 100 = 9 \text{ m} \)
- Answer: 9 m

6. 120 mm = ____ cm
- \( 120 \text{ mm} \div 10 = 12 \text{ cm} \)
- Answer: 12 cm

7. 7 km = ____ m
- \( 7 \text{ km} \times 1000 = 7000 \text{ m} \)
- Answer: 7000 m

8. 14 cm = ____ mm
- \( 14 \text{ cm} \times 10 = 140 \text{ mm} \)
- Answer: 140 mm

9. 12 m = ____ cm
- \( 12 \text{ m} \times 100 = 1200 \text{ cm} \)
- Answer: 1200 cm

10. ____ km = 13,000 m
- \( 13,000 \text{ m} \div 1000 = 13 \text{ km} \)
- Answer: 13 km

11. ____ cm = 130 mm
- \( 130 \text{ mm} \div 10 = 13 \text{ cm} \)
- Answer: 13 cm

12. 1400 cm = ____ m
- \( 1400 \text{ cm} \div 100 = 14 \text{ m} \)
- Answer: 14 m

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#### Part 2: Which is the most? Circle the largest amount in each box

We need to compare the values in each box and identify the largest one.

1. Box 1:
- \( 100 \text{ m} \)
- \( 1 \text{ km} \)
- \( 1000 \text{ cm} \)
- Conversion: \( 1 \text{ km} = 1000 \text{ m} \), \( 1000 \text{ cm} = 10 \text{ m} \)
- Largest: \( 1 \text{ km} \)
- Answer: 1 km

2. Box 2:
- \( 3 \text{ km} \)
- \( 2850 \text{ m} \)
- \( 5000 \text{ cm} \)
- Conversion: \( 3 \text{ km} = 3000 \text{ m} \), \( 5000 \text{ cm} = 50 \text{ m} \)
- Largest: \( 3 \text{ km} \)
- Answer: 3 km

3. Box 3:
- \( 380 \text{ cm} \)
- \( 4000 \text{ mm} \)
- \( 3 \text{ m} \)
- Conversion: \( 4000 \text{ mm} = 4 \text{ m} \), \( 380 \text{ cm} = 3.8 \text{ m} \)
- Largest: \( 4 \text{ m} \)
- Answer: 4000 mm

4. Box 4:
- \( 9020 \text{ m} \)
- \( 20,000 \text{ cm} \)
- \( 9 \text{ km} \)
- Conversion: \( 20,000 \text{ cm} = 200 \text{ m} \), \( 9 \text{ km} = 9000 \text{ m} \)
- Largest: \( 9020 \text{ m} \)
- Answer: 9020 m

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#### Part 3: Use greater than (>), less than (<), or equals (=) to compare the amounts

We compare the given values using their equivalent units.

1. 3 km > 2000 m
- \( 3 \text{ km} = 3000 \text{ m} \)
- \( 3000 \text{ m} > 2000 \text{ m} \)
- Answer: >

2. 1000 m = 1 km
- \( 1 \text{ km} = 1000 \text{ m} \)
- Answer: =

3. 5 cm < 50 mm
- \( 5 \text{ cm} = 50 \text{ mm} \)
- Answer: =

4. 300 m < 3 km
- \( 3 \text{ km} = 3000 \text{ m} \)
- \( 300 \text{ m} < 3000 \text{ m} \)
- Answer: <

5. 7 m > 500 cm
- \( 7 \text{ m} = 700 \text{ cm} \)
- \( 700 \text{ cm} > 500 \text{ cm} \)
- Answer: >

6. 6 cm > 80 mm
- \( 6 \text{ cm} = 60 \text{ mm} \)
- \( 60 \text{ mm} > 80 \text{ mm} \)
- Answer: <

7. 30 mm < 3 cm
- \( 3 \text{ cm} = 30 \text{ mm} \)
- Answer: <

8. 800 cm = 7 m
- \( 7 \text{ m} = 700 \text{ cm} \)
- Answer: >

9. 40 cm < 4 m
- \( 4 \text{ m} = 400 \text{ cm} \)
- Answer: <

10. 5 km > 4900 m
- \( 5 \text{ km} = 5000 \text{ m} \)
- \( 5000 \text{ m} > 4900 \text{ m} \)
- Answer: >

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Final Answers:

1. 5000 m
2. 6 m
3. 80 mm
4. 4 km
5. 9 m
6. 12 cm
7. 7000 m
8. 140 mm
9. 1200 cm
10. 13 km
11. 13 cm
12. 14 m

Part 2:
1. 1 km
2. 3 km
3. 4000 mm
4. 9020 m

Part 3:
1. >
2. =
3. =
4. <
5. >
6. <
7. <
8. >
9. <
10. >

Final Boxed Answer:
\[
\boxed{
\begin{array}{l}
\text{Part 1: } 5000, 6, 80, 4, 9, 12, 7000, 140, 1200, 13, 13, 14 \\
\text{Part 2: } 1 \text{ km}, 3 \text{ km}, 4000 \text{ mm}, 9020 \text{ m} \\
\text{Part 3: } >, =, =, <, >, <, <, >, <, >
\end{array}
}
\]