Metric system conversion worksheet with problems involving decimeters, liters, grams, and centigrams.

Let's solve each part of the worksheet step by step using the metric system and the conversion factors provided.

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I. Using the prefix "deci"

Key factor:
- 1 decimeter (dm) = 0.1 meter → or 10 dm = 1 m
- 1 decigram (dg) = 0.1 gram → or 10 dg = 1 g
- 1 deciliter (dL) = 0.1 liter → or 10 dL = 1 L

We’ll use these to convert units.

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#### a) 2.5 deciliters → ? liters

We know:
> 10 deciliters = 1 liter
So, to convert deciliters to liters: divide by 10

$$
2.5 \text{ dL} = \frac{2.5}{10} = 0.25 \text{ L}
$$

✔ Answer: 0.25 liter

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#### b) 115 decimeters → ? meters

We know:
> 10 decimeters = 1 meter
So, divide by 10

$$
115 \text{ dm} = \frac{115}{10} = 11.5 \text{ m}
$$

✔ Answer: 11.5 meters

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#### c) 0.6 liter → ? deciliters

We know:
> 1 liter = 10 deciliters
So, multiply by 10

$$
0.6 \text{ L} = 0.6 \times 10 = 6 \text{ dL}
$$

✔ Answer: 6 deciliters

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#### d) 0.75 meter → ? decimeters

We know:
> 1 meter = 10 decimeters
So, multiply by 10

$$
0.75 \text{ m} = 0.75 \times 10 = 7.5 \text{ dm}
$$

✔ Answer: 7.5 decimeters

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II. Using the prefix "centi"

Key factor:
- 1 centimeter (cm) = 0.01 meter → or 100 cm = 1 m
- 1 centigram (cg) = 0.01 gram → or 100 cg = 1 g
- 1 centiliter (cL) = 0.01 liter → or 100 cL = 1 L

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#### e) 32 decigrams → ? grams

We know:
> 10 decigrams = 1 gram
So, divide by 10

$$
32 \text{ dg} = \frac{32}{10} = 3.2 \text{ g}
$$

✔ Answer: 3.2 grams

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#### f) 0.17 gram → ? decigrams

We know:
> 1 gram = 10 decigrams
So, multiply by 10

$$
0.17 \text{ g} = 0.17 \times 10 = 1.7 \text{ dg}
$$

✔ Answer: 1.7 decigrams

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✔ Final Answers:

I. Using "deci" prefix:

a) $ 2.5 \text{ dL} = \boxed{0.25} \text{ liter} $

b) $ 115 \text{ dm} = \boxed{11.5} \text{ meters} $

c) $ 0.6 \text{ L} = \boxed{6} \text{ deciliters} $

d) $ 0.75 \text{ m} = \boxed{7.5} \text{ decimeters} $

II. Using "centi" prefix:

e) $ 32 \text{ dg} = \boxed{3.2} \text{ grams} $

f) $ 0.17 \text{ g} = \boxed{1.7} \text{ decigrams} $

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🔍 Explanation Summary:

- The prefix "deci-" means 1/10, so:
- To convert from deci to base unit: divide by 10
- To convert from base unit to deci: multiply by 10

- The prefix "centi-" means 1/100, so:
- To convert from centi to base unit: divide by 100
- To convert from base unit to centi: multiply by 100

But in this worksheet, only "deci" is used for all conversions — even though part II mentions "centi", the actual problems (e and f) are still about decigrams, not centigrams.

So, we applied the "deci" conversion rules consistently.

Let me know if you'd like a version with centi-conversions too!