Metric Dimensional Analysis Practice 1 worksheet featuring unit conversion problems using the factor label method, with examples and exercises.

Let's solve each problem step-by-step using dimensional analysis (factor label method). We'll set up the conversions clearly, round to correct significant digits, and include units.

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Simple Metric Conversion: Set 1

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#### 1. Convert 135 meters (m) to kilometers (km).

We know:
- 1 km = 1000 m

So:

$$
135\ \text{m} \times \frac{1\ \text{km}}{1000\ \text{m}} = 0.135\ \text{km}
$$

✔ Answer: $ 0.135\ \text{km} $

(3 significant figures — same as 135)

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#### 2. A piece of property is found to be 399 decimeters (dm) long. Find the length in centimeters (cm).

We know:
- 1 dm = 10 cm

So:

$$
399\ \text{dm} \times \frac{10\ \text{cm}}{1\ \text{dm}} = 3990\ \text{cm}
$$

✔ Answer: $ 3990\ \text{cm} $

(3 significant figures — same as 399)

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#### 3. How many millimeters are there in $ 5.57 \times 10^3 $ meters (m)?

We know:
- 1 m = 1000 mm

So:

$$
5.57 \times 10^3\ \text{m} \times \frac{1000\ \text{mm}}{1\ \text{m}} = 5.57 \times 10^6\ \text{mm}
$$

✔ Answer: $ 5.57 \times 10^6\ \text{mm} $

(3 significant figures — same as 5.57)

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#### 4. A book is found to have a mass of 0.8341 kilogram (kg). Calculate its mass in grams (g).

We know:
- 1 kg = 1000 g

So:

$$
0.8341\ \text{kg} \times \frac{1000\ \text{g}}{1\ \text{kg}} = 834.1\ \text{g}
$$

✔ Answer: $ 834.1\ \text{g} $

(4 significant figures — same as 0.8341)

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#### 5. Calculate the number of micrograms (μg) in 0.000721 gram (g).

We know:
- 1 g = $ 1 \times 10^6 $ μg

So:

$$
0.000721\ \text{g} \times \frac{1 \times 10^6\ \mu\text{g}}{1\ \text{g}} = 721\ \mu\text{g}
$$

✔ Answer: $ 721\ \mu\text{g} $

(3 significant figures — same as 0.000721 → 7.21 × 10⁻⁴)

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✔ Final Answers Summary:

1. $ 135\ \text{m} = 0.135\ \text{km} $
2. $ 399\ \text{dm} = 3990\ \text{cm} $
3. $ 5.57 \times 10^3\ \text{m} = 5.57 \times 10^6\ \text{mm} $
4. $ 0.8341\ \text{kg} = 834.1\ \text{g} $
5. $ 0.000721\ \text{g} = 721\ \mu\text{g} $

All answers are rounded to correct significant figures and include proper units.

Let me know if you'd like help with the Introduction & Examples problems too!