Metric Conversions worksheet - Free Printable

Problem Explanation and Solution

The worksheet involves converting metric units of length, comparing lengths, and determining the largest amount in each set. 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 conversion problem.

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

##### 2) 600 cm = ____ m
- Conversion: \( 1 \text{ m} = 100 \text{ cm} \) or \( 1 \text{ cm} = \frac{1}{100} \text{ m} \)
- Calculation: \( 600 \text{ cm} \div 100 = 6 \text{ m} \)
- Answer: \( 6 \text{ m} \)

##### 3) 8 cm = ____ mm
- Conversion: \( 1 \text{ cm} = 10 \text{ mm} \)
- Calculation: \( 8 \text{ cm} \times 10 = 80 \text{ mm} \)
- Answer: \( 80 \text{ mm} \)

##### 4) ____ km = 4000 m
- Conversion: \( 1 \text{ km} = 1000 \text{ m} \) or \( 1 \text{ m} = \frac{1}{1000} \text{ km} \)
- Calculation: \( 4000 \text{ m} \div 1000 = 4 \text{ km} \)
- Answer: \( 4 \text{ km} \)

##### 5) ____ m = 900 cm
- Conversion: \( 1 \text{ m} = 100 \text{ cm} \) or \( 1 \text{ cm} = \frac{1}{100} \text{ m} \)
- Calculation: \( 900 \text{ cm} \div 100 = 9 \text{ m} \)
- Answer: \( 9 \text{ m} \)

##### 6) 120 mm = ____ cm
- Conversion: \( 1 \text{ cm} = 10 \text{ mm} \) or \( 1 \text{ mm} = \frac{1}{10} \text{ cm} \)
- Calculation: \( 120 \text{ mm} \div 10 = 12 \text{ cm} \)
- Answer: \( 12 \text{ cm} \)

##### 7) 7 km = ____ m
- Conversion: \( 1 \text{ km} = 1000 \text{ m} \)
- Calculation: \( 7 \text{ km} \times 1000 = 7000 \text{ m} \)
- Answer: \( 7000 \text{ m} \)

##### 8) 14 cm = ____ mm
- Conversion: \( 1 \text{ cm} = 10 \text{ mm} \)
- Calculation: \( 14 \text{ cm} \times 10 = 140 \text{ mm} \)
- Answer: \( 140 \text{ mm} \)

##### 9) 12 m = ____ cm
- Conversion: \( 1 \text{ m} = 100 \text{ cm} \)
- Calculation: \( 12 \text{ m} \times 100 = 1200 \text{ cm} \)
- Answer: \( 1200 \text{ cm} \)

##### 10) ____ km = 13,000 m
- Conversion: \( 1 \text{ km} = 1000 \text{ m} \) or \( 1 \text{ m} = \frac{1}{1000} \text{ km} \)
- Calculation: \( 13,000 \text{ m} \div 1000 = 13 \text{ km} \)
- Answer: \( 13 \text{ km} \)

##### 11) ____ cm = 130 mm
- Conversion: \( 1 \text{ cm} = 10 \text{ mm} \) or \( 1 \text{ mm} = \frac{1}{10} \text{ cm} \)
- Calculation: \( 130 \text{ mm} \div 10 = 13 \text{ cm} \)
- Answer: \( 13 \text{ cm} \)

##### 12) 1400 cm = ____ m
- Conversion: \( 1 \text{ m} = 100 \text{ cm} \) or \( 1 \text{ cm} = \frac{1}{100} \text{ m} \)
- Calculation: \( 1400 \text{ cm} \div 100 = 14 \text{ m} \)
- Answer: \( 14 \text{ m} \)

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

We need to compare the given lengths and identify the largest one in each set.

##### Set 1:
- 100 m
- 1 km (Circle this because \( 1 \text{ km} = 1000 \text{ m} \))
- 1000 cm (Note: \( 1000 \text{ cm} = 10 \text{ m} \))

##### Set 2:
- 3 km (Circle this because \( 3 \text{ km} = 3000 \text{ m} \))
- 2850 m
- 5000 cm (Note: \( 5000 \text{ cm} = 50 \text{ m} \))

##### Set 3:
- 380 cm (Note: \( 380 \text{ cm} = 3.8 \text{ m} \))
- 4000 mm (Note: \( 4000 \text{ mm} = 4 \text{ m} \))
- 3 m

##### Set 4:
- 9020 m
- 20,000 cm (Note: \( 20,000 \text{ cm} = 200 \text{ m} \))
- 9 km (Circle this because \( 9 \text{ km} = 9000 \text{ m} \))

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

We compare the given lengths using their equivalent values.

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

##### 2) 1000 m = 1 km
- Conversion: \( 1 \text{ km} = 1000 \text{ m} \)
- Comparison: \( 1000 \text{ m} = 1000 \text{ m} \)
- Answer: \( = \)

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

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

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

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

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

##### 8) 800 cm < 7 m
- Conversion: \( 7 \text{ m} = 700 \text{ cm} \)
- Comparison: \( 800 \text{ cm} > 700 \text{ cm} \)
- Answer: \( > \)

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

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

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Final Answers

#### Part 1:
1. \( 5000 \text{ m} \)
2. \( 6 \text{ m} \)
3. \( 80 \text{ mm} \)
4. \( 4 \text{ km} \)
5. \( 9 \text{ m} \)
6. \( 12 \text{ cm} \)
7. \( 7000 \text{ m} \)
8. \( 140 \text{ mm} \)
9. \( 1200 \text{ cm} \)
10. \( 13 \text{ km} \)
11. \( 13 \text{ cm} \)
12. \( 14 \text{ m} \)

#### Part 2:
- Set 1: \( 1 \text{ km} \)
- Set 2: \( 3 \text{ km} \)
- Set 3: \( 4000 \text{ mm} \)
- Set 4: \( 9 \text{ km} \)

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

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