Worksheet for practicing unit conversions, including length, mass, and volume, with instructions to show work and use proper significant figures.

Let's solve each of the unit conversion problems step by step, showing the setup with units and ensuring the correct number of significant figures.

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1) 0.30 m = ________ mm

We know:
1 m = 1000 mm

$$
0.30\ \text{m} \times \frac{1000\ \text{mm}}{1\ \text{m}} = 300\ \text{mm}
$$

Answer: 300 mm
(Significant figures: 0.30 has 2 sig figs → answer should have 2 sig figs → 3.0 × 10² mm, but 300 is acceptable as it implies 2 sig figs when written without decimal)

✔ Final Answer: 300 mm

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2) 5.00 mm = ________ cm

We know:
1 cm = 10 mm

$$
5.00\ \text{mm} \times \frac{1\ \text{cm}}{10\ \text{mm}} = 0.500\ \text{cm}
$$

Answer: 0.500 cm
(3 sig figs — preserved)

✔ Final Answer: 0.500 cm

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3) 10.0 cm = ________ in

We know:
1 inch = 2.54 cm (exact)

$$
10.0\ \text{cm} \times \frac{1\ \text{in}}{2.54\ \text{cm}} = 3.937\ \text{in} \approx 3.94\ \text{in}
$$

Round to 3 sig figs (10.0 has 3 sig figs)

✔ Final Answer: 3.94 in

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4) 2.00 km = ________ m

We know:
1 km = 1000 m

$$
2.00\ \text{km} \times \frac{1000\ \text{m}}{1\ \text{km}} = 2000\ \text{m}
$$

But we must express with proper sig figs: 2.00 has 3 sig figs → 2000 m should be written as 2.00 × 10³ m

✔ Final Answer: 2.00 × 10³ m

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5) 33.4 L = ________ mL

We know:
1 L = 1000 mL

$$
33.4\ \text{L} \times \frac{1000\ \text{mL}}{1\ \text{L}} = 33,400\ \text{mL}
$$

33.4 has 3 sig figs → answer: 3.34 × 10⁴ mL

✔ Final Answer: 3.34 × 10⁴ mL

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6) 15.0 lb = ________ kg

(use 2.20 lb = 1 kg)

$$
15.0\ \text{lb} \times \frac{1\ \text{kg}}{2.20\ \text{lb}} = 6.818\ \text{kg} \approx 6.82\ \text{kg}
$$

15.0 has 3 sig figs; 2.20 has 3 → answer has 3 sig figs

✔ Final Answer: 6.82 kg

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7) 0.400 L = ________ mL

$$
0.400\ \text{L} \times \frac{1000\ \text{mL}}{1\ \text{L}} = 400.\ \text{mL}
$$

0.400 has 3 sig figs → 400. mL (with decimal point to indicate 3 sig figs)

✔ Final Answer: 400. mL

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8) 5.00 g = ________ kg

We know:
1 kg = 1000 g

$$
5.00\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 0.00500\ \text{kg}
$$

→ 5.00 × 10⁻³ kg

✔ Final Answer: 5.00 × 10⁻³ kg

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9) 1.00 yd = ________ cm

(3 ft = 1 yard, exactly)

We know:
1 yard = 3 ft
1 ft = 12 in
1 in = 2.54 cm

So:

$$
1.00\ \text{yd} \times \frac{3\ \text{ft}}{1\ \text{yd}} \times \frac{12\ \text{in}}{1\ \text{ft}} \times \frac{2.54\ \text{cm}}{1\ \text{in}} = ?
$$

Step-by-step:

- 3 × 12 = 36 inches
- 36 × 2.54 = 91.44 cm

All conversions are exact except 2.54 cm/in (defined), so we keep 3 sig figs from 1.00 yd

✔ Final Answer: 91.4 cm

Wait — actually, since 1.00 yd has 3 sig figs, and all conversion factors are exact or defined, we can report to 3 sig figs:

91.44 → 91.4 cm

But let’s double-check:
1 yard = 0.9144 meters → 91.44 cm → yes.

So 91.4 cm (3 sig figs)

✔ Final Answer: 91.4 cm

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10) 6.35 g = ________ kg

$$
6.35\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 0.00635\ \text{kg} = 6.35 \times 10^{-3}\ \text{kg}
$$

✔ Final Answer: 6.35 × 10⁻³ kg

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11) 8.245 L = ________ mL

$$
8.245\ \text{L} \times \frac{1000\ \text{mL}}{1\ \text{L}} = 8245\ \text{mL}
$$

8.245 has 4 sig figs → 8245 mL (all digits are significant)

✔ Final Answer: 8245 mL

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12) 16.9 fl. oz = ________ L

(0.0338 fl. oz = 1 mL)

First, convert fl. oz → mL:

$$
16.9\ \text{fl. oz} \times \frac{1\ \text{mL}}{0.0338\ \text{fl. oz}} = \frac{16.9}{0.0338} = 500.0\ \text{mL} \approx 500. mL
$$

Now convert mL → L:

$$
500.\ \text{mL} \times \frac{1\ \text{L}}{1000\ \text{mL}} = 0.500\ \text{L}
$$

16.9 has 3 sig figs; 0.0338 has 3 sig figs → final answer should have 3 sig figs

✔ Final Answer: 0.500 L

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13) 1.00 cm = ________ m

$$
1.00\ \text{cm} \times \frac{1\ \text{m}}{100\ \text{cm}} = 0.0100\ \text{m}
$$

→ 1.00 × 10⁻² m

✔ Final Answer: 0.0100 m

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14) 345 g = ________ kg

$$
345\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 0.345\ \text{kg}
$$

345 has 3 sig figs → 0.345 kg

✔ Final Answer: 0.345 kg

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## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1) | 300 mm |
| 2) | 0.500 cm |
| 3) | 3.94 in |
| 4) | 2.00 × 10³ m |
| 5) | 3.34 × 10⁴ mL |
| 6) | 6.82 kg |
| 7) | 400. mL |
| 8) | 5.00 × 10⁻³ kg |
| 9) | 91.4 cm |
| 10) | 6.35 × 10⁻³ kg |
| 11) | 8245 mL |
| 12) | 0.500 L |
| 13) | 0.0100 m |
| 14) | 0.345 kg |

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📌 Notes on Significant Figures:

- When multiplying/dividing, the result has the same number of sig figs as the least precise measurement.
- Exact conversions (like 1000 mL = 1 L) do not affect sig figs.
- Use scientific notation when needed to clearly show sig figs.

Let me know if you'd like a printable version or explanation for any specific problem!