Solved Unit Conversions Worksheet mm Complete each of the | Chegg.com - Free Printable

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

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1) 0.30 m = ______ mm

Conversion factor:
1 m = 1000 mm

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

- Significant figures: 0.30 has 2 sig figs → answer should have 2 sig figs.
- 300 mm → 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

Conversion factor:
1 cm = 10 mm

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

- 5.00 has 3 sig figs → answer has 3 sig figs.

✔ Answer: 0.500 cm

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3) 10.0 in = ______ cm

Conversion factor:
1 inch = 2.54 cm (exact)

Setup:
$$
10.0 \, \text{in} \times \frac{2.54 \, \text{cm}}{1 \, \text{in}} = 25.4 \, \text{cm}
$$

- 10.0 has 3 sig figs → answer has 3 sig figs.

✔ Answer: 25.4 cm

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4) 2.00 km = ______ m

Conversion factor:
1 km = 1000 m

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

- 2.00 has 3 sig figs → 2000 m must be written as 2.00 × 10³ m to preserve 3 sig figs.

✔ Answer: 2.00 × 10³ m

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5) 33.4 L = ______ mL

Conversion factor:
1 L = 1000 mL

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

- 33.4 has 3 sig figs → answer is 3.34 × 10⁴ mL

✔ Answer: 3.34 × 10⁴ mL

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6) 15.0 lb = ______ kg

(Use 2.20 lb = 1 kg)

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

- 15.0 has 3 sig figs, 2.20 has 3 sig figs → answer has 3 sig figs.
- Round 6.818 to 6.82 kg

✔ Answer: 6.82 kg

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7) 0.400 L = ______ mL

Conversion factor:
1 L = 1000 mL

Setup:
$$
0.400 \, \text{L} \times \frac{1000 \, \text{mL}}{1 \, \text{L}} = 400 \, \text{mL}
$$

- 0.400 has 3 sig figs → 400 mL must be written as 4.00 × 10² mL

✔ Answer: 4.00 × 10² mL

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8) 5.00 g = ______ kg

Conversion factor:
1 kg = 1000 g

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

- 5.00 has 3 sig figs → write as 5.00 × 10⁻³ kg

✔ Answer: 5.00 × 10⁻³ kg

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9) 1.00 yd = ______ cm

(Given: 1 ft = 1 yard, exactly)
Wait — this seems incorrect. Actually:
1 yard = 3 feet, and 1 foot = 12 inches, and 1 inch = 2.54 cm

So:
- 1 yard = 3 ft
- 1 ft = 12 in → 3 ft = 36 in
- 1 in = 2.54 cm → 36 in = 36 × 2.54 = ?

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

Calculate:
- 3 × 12 = 36
- 36 × 2.54 = 91.44 cm

- 1.00 has 3 sig figs → answer is 91.4 cm? Wait — but 2.54 is exact for conversion?

Actually, 2.54 cm/in is defined, so it's exact. The limiting sig figs come from 1.00 yd → 3 sig figs.

So:
- 91.44 cm → round to 91.4 cm? But 36 is exact (from definition), so only 1.00 limits.

But wait: 3 ft/yd and 12 in/ft are exact, and 2.54 cm/in is exact, so the only measurement is 1.00 yd → 3 sig figs.

So 91.44 cm → rounded to 91.4 cm?

Wait: 36 × 2.54 = 91.44 → but since all conversions are exact, we keep 3 sig figs → 91.4 cm?

But actually, 91.44 has 4 digits, but we’re allowed to keep 3 sig figs because input was 1.00.

Wait — but 1.00 yd → 3 sig figs → result should have 3 sig figs.

So 91.44 → 91.4 cm? No — 91.44 rounded to 3 sig figs is 91.4 cm.

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

So if input is 1.00 yd (3 sig figs), then:

→ 91.4 cm (3 sig figs)

✔ Answer: 91.4 cm

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10) 6.35 g = ______ kg

Conversion factor:
1 kg = 1000 g

Setup:
$$
6.35 \, \text{g} \times \frac{1 \, \text{kg}}{1000 \, \text{g}} = 0.00635 \, \text{kg}
$$

- 6.35 has 3 sig figs → 6.35 × 10⁻³ kg

✔ Answer: 6.35 × 10⁻³ kg

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11) 8.45 L = ______ mL

Conversion factor:
1 L = 1000 mL

Setup:
$$
8.45 \, \text{L} \times \frac{1000 \, \text{mL}}{1 \, \text{L}} = 8450 \, \text{mL}
$$

- 8.45 has 3 sig figs → write as 8.45 × 10³ mL

✔ Answer: 8.45 × 10³ mL

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12) 16.9 fl. oz = ______ L

(Given: 0.0338 fl. oz = 1 mL)

We need to convert fl. oz → mL → L

First, use:
- 1 mL = 0.0338 fl. oz → so 1 fl. oz = 1 / 0.0338 mL ≈ 29.5858 mL

But better to do:

Setup:
$$
16.9 \, \text{fl. oz} \times \frac{1 \, \text{mL}}{0.0338 \, \text{fl. oz}} = \frac{16.9}{0.0338} \, \text{mL}
$$

Calculate:
$$
\frac{16.9}{0.0338} = 500.0 \, \text{mL} \quad (\text{approximately})
$$

Check: 0.0338 × 500 = 16.9 → yes!

So 16.9 fl. oz = 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 → answer should have 3 sig figs → 0.500 L

✔ Answer: 0.500 L

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13) 1.00 cm = ______ m

Conversion factor:
1 m = 100 cm

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

- 1.00 has 3 sig figs → answer is 1.00 × 10⁻² m

✔ Answer: 1.00 × 10⁻² m

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14) 345 g = ______ kg

Conversion factor:
1 kg = 1000 g

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

- 345 has 3 sig figs → 0.345 kg has 3 sig figs

✔ Answer: 0.345 kg

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1) 0.30 m | 3.0 × 10² mm |
| 2) 5.00 mm | 0.500 cm |
| 3) 10.0 in | 25.4 cm |
| 4) 2.00 km | 2.00 × 10³ m |
| 5) 33.4 L | 3.34 × 10⁴ mL |
| 6) 15.0 lb | 6.82 kg |
| 7) 0.400 L | 4.00 × 10² mL |
| 8) 5.00 g | 5.00 × 10⁻³ kg |
| 9) 1.00 yd | 91.4 cm |
| 10) 6.35 g | 6.35 × 10⁻³ kg |
| 11) 8.45 L | 8.45 × 10³ mL |
| 12) 16.9 fl. oz | 0.500 L |
| 13) 1.00 cm | 1.00 × 10⁻² m |
| 14) 345 g | 0.345 kg |

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