Unit conversion guide - Unit Conversions Worksheet Complete each ... - Free Printable

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

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

- 0.30 has 2 significant figures
- Answer: 300 mm (2 sig figs → written as 3.0 × 10² mm to show 2 sig figs)

✔ Answer: 3.0 × 10² mm

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2) 5.00 mm = ________ cm

We know:
1 cm = 10 mm

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

- 5.00 has 3 sig figs → answer must have 3 sig figs

✔ Answer: 0.500 cm

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3) 10.0 cm = ________ in

We know:
1 inch = 2.54 cm (exact)

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

- 10.0 has 3 sig figs → round to 3 sig figs

→ 3.94 in

✔ Answer: 3.94 in

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4) 2.00 km = ________ m

We know:
1 km = 1000 m

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

- 2.00 has 3 sig figs → write as 2.00 × 10³ m

✔ 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

✔ Answer: 3.34 × 10⁴ mL

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6) 15.0 lb = ________ kg

(use 2.20 lb = 1 kg)

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

- 15.0 has 3 sig figs, 2.20 has 3 → answer has 3 sig figs

→ 6.82 kg

✔ 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)

✔ 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 has 3 sig figs → 0.00500 kg (3 sig figs)

✔ Answer: 5.00 × 10⁻³ kg

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9) 1.00 yd = ________ cm

(3 ft = 1 yard, exactly)

We know:
- 1 yd = 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 in
- 36 × 2.54 = 91.44 cm

→ 91.44 cm

- 1.00 has 3 sig figs → answer: 91.4 cm (3 sig figs)

✔ 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 has 3 sig figs → 6.35 × 10⁻³ kg

✔ 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)

✔ Answer: 8245 mL

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12) 16.9 fl. oz = ________ L

(0.0338 fl. oz = 1 mL)

First, convert fl. oz to mL:

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

Now convert mL to L:

$$
500.0\ \text{mL} \times \frac{1\ \text{L}}{1000\ \text{mL}} = 0.5000\ \text{L}
$$

But let’s do it directly:

$$
16.9\ \text{fl. oz} \times \frac{1\ \text{mL}}{0.0338\ \text{fl. oz}} \times \frac{1\ \text{L}}{1000\ \text{mL}} = ?
$$

$$
= \frac{16.9}{0.0338 \times 1000} = \frac{16.9}{33.8} = 0.500\ \text{L}
$$

- 16.9 has 3 sig figs, 0.0338 has 3 → answer should have 3 sig figs

✔ Answer: 0.500 L

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13) 1.00 cm = ________ m

We know:
1 m = 100 cm

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

- 1.00 has 3 sig figs → 0.0100 m (3 sig figs)

✔ Answer: 1.00 × 10⁻² 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

✔ Answer: 0.345 kg

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## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1) | 3.0 × 10² 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) | 1.00 × 10⁻² m |
| 14) | 0.345 kg |

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