metric conversion worksheet
1. 5.712 g = ______ kg
2. 222.7 l = ______ dl
3. 16.45 m = ______ cm
4. 39.56 g = ______ mg
5. 10.5 g = ______ dkg
6. 3.54 mg = ______ dg
7. 28.6 g = ______ hg
8. 910 m = ______ dm
9. 0.006700 kg = ______ cg
10. 1488 cm = ______ hm
11. 42.68 l = ______ kl
12. 2.78 cm = ______ km
13. 5.44 m = ______ cm
14. 15.82 ml = ______ cm³

Question

Accepted Answer

### Problem 1: $ 5.712 \, \text{g} = \_\_\_\_\_ \, \text{kg} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{kg} = 1000 \, \text{g} $, so to convert grams to kilograms, we divide by $ 1000 $ (or multiply by $ 10^{-3} $).
## Step 2: Perform the conversion
$ 5.712 \, \text{g} \times \frac{1 \, \text{kg}}{1000 \, \text{g}} = 5.712 \times 10^{-3} \, \text{kg} = 0.005712 \, \text{kg} $
# Answer:
$ 0.005712 $

### Problem 2: $ 222.7 \, \text{L} = \_\_\_\_\_ \, \text{dL} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{L} = 10 \, \text{dL} $, so to convert liters to deciliters, we multiply by $ 10 $.
## Step 2: Perform the conversion
$ 222.7 \, \text{L} \times \frac{10 \, \text{dL}}{1 \, \text{L}} = 222.7 \times 10 = 2227 \, \text{dL} $
# Answer:
$ 2227 $

### Problem 3: $ 16.45 \, \text{m} = \_\_\_\_\_ \, \text{cm} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{m} = 100 \, \text{cm} $, so to convert meters to centimeters, we multiply by $ 100 $.
## Step 2: Perform the conversion
$ 16.45 \, \text{m} \times \frac{100 \, \text{cm}}{1 \, \text{m}} = 16.45 \times 100 = 1645 \, \text{cm} $
# Answer:
$ 1645 $

### Problem 4: $ 39.56 \, \text{g} = \_\_\_\_\_ \, \text{mg} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{g} = 1000 \, \text{mg} $, so to convert grams to milligrams, we multiply by $ 1000 $ (or $ 10^{3} $).
## Step 2: Perform the conversion
$ 39.56 \, \text{g} \times \frac{1000 \, \text{mg}}{1 \, \text{g}} = 39.56 \times 1000 = 39560 \, \text{mg} $
# Answer:
$ 39560 $

### Problem 5: $ 10.5 \, \text{g} = \_\_\_\_\_ \, \text{dkg} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{dkg} = 10 \, \text{g} $, so to convert grams to decagrams, we divide by $ 10 $ (or multiply by $ 10^{-1} $).
## Step 2: Perform the conversion
$ 10.5 \, \text{g} \times \frac{1 \, \text{dkg}}{10 \, \text{g}} = \frac{10.5}{10} = 1.05 \, \text{dkg} $
# Answer:
$ 1.05 $

### Problem 6: $ 3.54 \, \text{mg} = \_\_\_\_\_ \, \text{dg} $
# Explanation:
## Step 1: Recall the conversion factors
First, $ 1 \, \text{g} = 1000 \, \text{mg} $ and $ 1 \, \text{dg} = 0.1 \, \text{g} $ (or $ 1 \, \text{g} = 10 \, \text{dg} $). So, to convert milligrams to decigrams, we can use the chain: $ \text{mg} \to \text{g} \to \text{dg} $.
First, convert $ \text{mg} $ to $ \text{g} $: $ 3.54 \, \text{mg} = 3.54 \times 10^{-3} \, \text{g} $ (since $ 1 \, \text{mg} = 10^{-3} \, \text{g} $).
Then, convert $ \text{g} $ to $ \text{dg} $: $ 1 \, \text{g} = 10 \, \text{dg} $, so $ 3.54 \times 10^{-3} \, \text{g} \times 10 \, \text{dg/g} = 3.54 \times 10^{-2} \, \text{dg} = 0.0354 \, \text{dg} $
Alternatively, using the direct conversion factor: $ 1 \, \text{dg} = 100 \, \text{mg} $ (since $ 1 \, \text{dg} = 0.1 \, \text{g} = 0.1 \times 1000 \, \text{mg} = 100 \, \text{mg} $), so $ 3.54 \, \text{mg} \div 100 = 0.0354 \, \text{dg} $
## Step 2: Perform the conversion
$ 3.54 \, \text{mg} \times \frac{1 \, \text{dg}}{100 \, \text{mg}} = \frac{3.54}{100} = 0.0354 \, \text{dg} $
# Answer:
$ 0.0354 $

### Problem 7: $ 28.6 \, \text{g} = \_\_\_\_\_ \, \text{hg} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{hg} = 100 \, \text{g} $, so to convert grams to hectograms, we divide by $ 100 $ (or multiply by $ 10^{-2} $).
## Step 2: Perform the conversion
$ 28.6 \, \text{g} \times \frac{1 \, \text{hg}}{100 \, \text{g}} = \frac{28.6}{100} = 0.286 \, \text{hg} $
# Answer:
$ 0.286 $

### Problem 8: $ 910 \, \text{m} = \_\_\_\_\_ \, \text{dm} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{m} = 10 \, \text{dm} $, so to convert meters to decimeters, we multiply by $ 10 $.
## Step 2: Perform the conversion
$ 910 \, \text{m} \times \frac{10 \, \text{dm}}{1 \, \text{m}} = 910 \times 10 = 9100 \, \text{dm} $
# Answer:
$ 9100 $

### Problem 9: $ 0.006700 \, \text{kg} = \_\_\_\_\_ \, \text{cg} $
# Explanation:
## Step 1: Recall the conversion factors
We know that $ 1 \, \text{kg} = 1000 \, \text{g} $ and $ 1 \, \text{g} = 100 \, \text{cg} $. So, first convert $ \text{kg} $ to $ \text{g} $, then $ \text{g} $ to $ \text{cg} $.
First, $ 0.006700 \, \text{kg} \times 1000 \, \text{g/kg} = 6.700 \, \text{g} $
Then, $ 6.700 \, \text{g} \times 100 \, \text{cg/g} = 670.0 \, \text{cg} $
Alternatively, using the direct conversion factor: $ 1 \, \text{kg} = 10^{5} \, \text{cg} $ (since $ 1 \, \text{kg} = 1000 \, \text{g} = 1000 \times 100 \, \text{cg} = 100000 \, \text{cg} $), so $ 0.006700 \, \text{kg} \times 100000 \, \text{cg/kg} = 670.0 \, \text{cg} $
## Step 2: Perform the conversion
$ 0.006700 \, \text{kg} \times \frac{100000 \, \text{cg}}{1 \, \text{kg}} = 0.006700 \times 100000 = 670.0 \, \text{cg} $
# Answer:
$ 670.0 $

### Problem 10: $ 1488 \, \text{cm} = \_\_\_\_\_ \, \text{hm} $
# Explanation:
## Step 1: Recall the conversion factors
We know that $ 1 \, \text{m} = 100 \, \text{cm} $ and $ 1 \, \text{hm} = 100 \, \text{m} $. So, first convert $ \text{cm} $ to $ \text{m} $, then $ \text{m} $ to $ \text{hm} $.
First, $ 1488 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 14.88 \, \text{m} $
Then, $ 14.88 \, \text{m} \times \frac{1 \, \text{hm}}{100 \, \text{m}} = \frac{14.88}{100} = 0.1488 \, \text{hm} $
Alternatively, using the direct conversion factor: $ 1 \, \text{hm} = 10000 \, \text{cm} $ (since $ 1 \, \text{hm} = 100 \, \text{m} = 100 \times 100 \, \text{cm} = 10000 \, \text{cm} $), so $ 1488 \, \text{cm} \div 10000 = 0.1488 \, \text{hm} $
## Step 2: Perform the conversion
$ 1488 \, \text{cm} \times \frac{1 \, \text{hm}}{10000 \, \text{cm}} = \frac{1488}{10000} = 0.1488 \, \text{hm} $
# Answer:
$ 0.1488 $

### Problem 11: $ 42.68 \, \text{L} = \_\_\_\_\_ \, \text{kL} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{kL} = 1000 \, \text{L} $, so to convert liters to kiloliters, we divide by $ 1000 $ (or multiply by $ 10^{-3} $).
## Step 2: Perform the conversion
$ 42.68 \, \text{L} \times \frac{1 \, \text{kL}}{1000 \, \text{L}} = 42.68 \times 10^{-3} = 0.04268 \, \text{kL} $
# Answer:
$ 0.04268 $

### Problem 12: $ 2.78 \, \text{cm} = \_\_\_\_\_ \, \text{km} $
# Explanation:
## Step 1: Recall the conversion factors
We know that $ 1 \, \text{m} = 100 \, \text{cm} $, $ 1 \, \text{km} = 1000 \, \text{m} $. So, first convert $ \text{cm} $ to $ \text{m} $, then $ \text{m} $ to $ \text{km} $.
First, $ 2.78 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 0.0278 \, \text{m} $
Then, $ 0.0278 \, \text{m} \times \frac{1 \, \text{km}}{1000 \, \text{m}} = 0.0278 \times 10^{-3} = 2.78 \times 10^{-5} \, \text{km} $
Alternatively, using the direct conversion factor: $ 1 \, \text{km} = 10^{5} \, \text{cm} $ (since $ 1 \, \text{km} = 1000 \, \text{m} = 1000 \times 100 \, \text{cm} = 100000 \, \text{cm} $), so $ 2.78 \, \text{cm} \div 100000 = 2.78 \times 10^{-5} \, \text{km} $
## Step 2: Perform the conversion
$ 2.78 \, \text{cm} \times \frac{1 \, \text{km}}{100000 \, \text{cm}} = \frac{2.78}{100000} = 2.78 \times 10^{-5} \, \text{km} $
# Answer:
$ 2.78 \times 10^{-5} $ (or $ 0.0000278 $)

### Problem 13: $ 5.44 \, \text{m} = \_\_\_\_\_ \, \text{cm} $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{m} = 100 \, \text{cm} $, so to convert meters to centimeters, we multiply by $ 100 $.
## Step 2: Perform the conversion
$ 5.44 \, \text{m} \times \frac{100 \, \text{cm}}{1 \, \text{m}} = 5.44 \times 100 = 544 \, \text{cm} $
# Answer:
$ 544 $

### Problem 14: $ 15.82 \, \text{mL} = \_\_\_\_\_ \, \text{cm}^3 $
# Explanation:
## Step 1: Recall the conversion factor
We know that $ 1 \, \text{mL} = 1 \, \text{cm}^3 $ (this is a direct conversion in the metric system for volume).
## Step 2: Perform the conversion
Since $ 1 \, \text{mL} = 1 \, \text{cm}^3 $, then $ 15.82 \, \text{mL} = 15.82 \, \text{cm}^3 $
# Answer:
$ 15.82 $

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QUESTION IMAGE

Question

Explanation:

Problem 1: \( 5.712 \, \text{g} = \_\_\_\_\_ \, \text{kg} \)

Step 1: Recall the conversion factor

Step 2: Perform the conversion

Step 1: Recall the conversion factor

Step 2: Perform the conversion

Step 1: Recall the conversion factor

Step 2: Perform the conversion

Answer:

Problem 2: \( 222.7 \, \text{L} = \_\_\_\_\_ \, \text{dL} \)